{"id":35998,"date":"2026-01-10T18:40:42","date_gmt":"2026-01-10T18:40:42","guid":{"rendered":"https:\/\/toposuranos.com\/material\/?p=35998"},"modified":"2026-01-10T18:40:42","modified_gmt":"2026-01-10T18:40:42","slug":"%e0%a4%af%e0%a5%82%e0%a4%95%e0%a5%8d%e0%a4%b2%e0%a4%bf%e0%a4%a1%e0%a5%80%e0%a4%af-%e0%a4%b5%e0%a4%bf%e0%a4%ad%e0%a4%be%e0%a4%9c%e0%a4%a8-%e0%a4%95%e0%a4%be-%e0%a4%8f%e0%a4%b2%e0%a5%8d%e0%a4%97","status":"publish","type":"post","link":"https:\/\/toposuranos.com\/material\/hi\/%e0%a4%af%e0%a5%82%e0%a4%95%e0%a5%8d%e0%a4%b2%e0%a4%bf%e0%a4%a1%e0%a5%80%e0%a4%af-%e0%a4%b5%e0%a4%bf%e0%a4%ad%e0%a4%be%e0%a4%9c%e0%a4%a8-%e0%a4%95%e0%a4%be-%e0%a4%8f%e0%a4%b2%e0%a5%8d%e0%a4%97\/","title":{"rendered":"\u092f\u0942\u0915\u094d\u0932\u093f\u0921\u0940\u092f \u0935\u093f\u092d\u093e\u091c\u0928 \u0915\u093e \u090f\u0932\u094d\u0917\u094b\u0930\u093f\u0926\u094d\u092e"},"content":{"rendered":"<style>\np, ul, ol{\n  text-align: justify;\n}\nh1{\n  text-align:center;\n  text-transform: uppercase;\n}\nh2{\n  text-align:center;\n  text-transform: uppercase;\n  font-size:24pt;\n}\nh3{\n  text-align: center;\n  text-transform: uppercase;\n  font-size: 24px !important;\n}\n<\/style>\n<h1>\u0935\u093f\u092d\u093e\u091c\u0928 \u0915\u093e \u090f\u0932\u094d\u0917\u094b\u0930\u093f\u0926\u094d\u092e<\/h1>\n<p style=\"text-align:center;\"><em>\u0907\u0938 \u0915\u0915\u094d\u0937\u093e \u092e\u0947\u0902 \u0939\u092e <strong>\u0935\u093f\u092d\u093e\u091c\u0928 \u0915\u0947 \u090f\u0932\u094d\u0917\u094b\u0930\u093f\u0926\u094d\u092e<\/strong> \u0915\u094b \u0909\u0938 \u0938\u093f\u0926\u094d\u0927\u093e\u0902\u0924 \u0915\u0947 \u0930\u0942\u092a \u092e\u0947\u0902 \u0935\u093f\u0915\u0938\u093f\u0924 \u0915\u0930\u0947\u0902\u0917\u0947 \u091c\u094b \u092a\u0942\u0930\u094d\u0923\u093e\u0902\u0915\u094b\u0902 \u0915\u0947 \u0932\u093f\u090f \u0905\u0926\u094d\u0935\u093f\u0924\u0940\u092f \u0935\u093f\u0918\u091f\u0928 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">b=qa+r<\/span><\/span> \u0915\u094b \u0914\u092a\u091a\u093e\u0930\u093f\u0915 \u0930\u0942\u092a \u0926\u0947\u0924\u093e \u0939\u0948, \u091c\u0939\u093e\u0901 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">0\\le r&lt;|a|<\/span><\/span> \u0939\u094b\u0924\u093e \u0939\u0948\u0964 \u092a\u0939\u0932\u0947 \u092d\u093e\u0917\u092b\u0932 \u0914\u0930 \u0936\u0947\u0937 \u0915\u0940 <strong>\u0905\u0938\u094d\u0924\u093f\u0924\u094d\u0935<\/strong> \u0915\u094b \u0938\u093f\u0926\u094d\u0927 \u0915\u093f\u092f\u093e \u091c\u093e\u0924\u093e \u0939\u0948 \u0914\u0930 \u0909\u0938\u0915\u0947 \u092c\u093e\u0926 \u0909\u0928\u0915\u0940 <strong>\u090f\u0915\u093e\u0924\u094d\u092e\u0915\u0924\u093e<\/strong> \u0915\u094b\u0964 \u0905\u0902\u0924\u0924\u0903, \u0936\u0947\u0937 \u0915\u0947 \u0905\u0930\u094d\u0925 \u0915\u0940 \u0935\u094d\u092f\u093e\u0916\u094d\u092f\u093e \u0915\u0940 \u091c\u093e\u0924\u0940 \u0939\u0948, \u0938\u093f\u0926\u094d\u0927\u093e\u0902\u0924 \u0915\u094b \u0917\u0923\u0928\u093e \u0915\u0940 \u092a\u094d\u0930\u0915\u094d\u0930\u093f\u092f\u093e \u0915\u0947 \u0930\u0942\u092a \u092e\u0947\u0902 <strong>\u0932\u0902\u092c\u0947 \u0935\u093f\u092d\u093e\u091c\u0928 \u0915\u0947 \u090f\u0932\u094d\u0917\u094b\u0930\u093f\u0926\u094d\u092e<\/strong> \u0938\u0947 \u091c\u094b\u0921\u093c\u093e \u091c\u093e\u0924\u093e \u0939\u0948, \u0914\u0930 \u092e\u0949\u0921\u094d\u092f\u0942\u0932\u0930 \u0905\u0902\u0915\u0917\u0923\u093f\u0924 \u0924\u0925\u093e \u0938\u0902\u0917\u0923\u0915\u0940\u092f \u0905\u0928\u0941\u092a\u094d\u0930\u092f\u094b\u0917\u094b\u0902 \u0915\u0947 \u0938\u093e\u0925 \u0907\u0938\u0915\u0947 \u0938\u094d\u0935\u093e\u092d\u093e\u0935\u093f\u0915 \u0938\u0902\u092c\u0902\u0927 \u0915\u093e \u092a\u0942\u0930\u094d\u0935\u093e\u0928\u0941\u092e\u093e\u0928 \u0915\u093f\u092f\u093e \u091c\u093e\u0924\u093e \u0939\u0948\u0964<\/em><\/p>\n<p style=\"text-align:center;\"><strong>\u0905\u0927\u093f\u0917\u092e \u0909\u0926\u094d\u0926\u0947\u0936\u094d\u092f<\/strong><\/p>\n<p>\u0907\u0938 \u0915\u0915\u094d\u0937\u093e \u0915\u094b \u092a\u0942\u0930\u093e \u0915\u0930\u0928\u0947 \u092a\u0930 \u0935\u093f\u0926\u094d\u092f\u093e\u0930\u094d\u0925\u0940 \u0938\u0915\u094d\u0937\u092e \u0939\u094b\u0917\u093e:<\/p>\n<ol>\n<li><strong>\u092a\u0939\u091a\u093e\u0928\u0928\u0947<\/strong> \u0915\u0947 \u0932\u093f\u090f \u092a\u0942\u0930\u094d\u0923\u093e\u0902\u0915 \u0935\u093f\u092d\u093e\u091c\u0928 \u0915\u0947 \u092e\u0942\u0932\u092d\u0942\u0924 \u0938\u0902\u0915\u0932\u094d\u092a\u0928\u093e\u0913\u0902 \u0914\u0930 \u092d\u0942\u092e\u093f\u0915\u093e\u0913\u0902 (\u092d\u093e\u091c\u094d\u092f, \u092d\u093e\u091c\u0915, \u092d\u093e\u0917\u092b\u0932, \u0936\u0947\u0937) \u0924\u0925\u093e \u0935\u093f\u092d\u093e\u091c\u094d\u092f\u0924\u093e \u0915\u0940 \u0927\u093e\u0930\u0923\u093e \u0915\u094b \u090f\u0915 \u0938\u091f\u0940\u0915 \u0938\u094d\u0925\u093f\u0924\u093f \u0915\u0947 \u0930\u0942\u092a \u092e\u0947\u0902\u0964<\/li>\n<li><strong>\u0938\u092e\u091d\u093e\u0928\u0947<\/strong> \u0915\u0947 \u0932\u093f\u090f \u092f\u0942\u0915\u094d\u0932\u093f\u0921\u0940\u092f \u0935\u093f\u092d\u093e\u091c\u0928 \u0915\u0947 \u090f\u0932\u094d\u0917\u094b\u0930\u093f\u0926\u094d\u092e\/\u092a\u094d\u0930\u092e\u0947\u092f \u0915\u0947 \u0915\u0925\u0928 \u0915\u094b, \u091c\u093f\u0938\u092e\u0947\u0902 \u0936\u0947\u0937 \u0915\u094b \u0928\u093f\u0930\u094d\u0927\u093e\u0930\u093f\u0924 \u0915\u0930\u0928\u0947 \u0935\u093e\u0932\u0940 \u0936\u0930\u094d\u0924\u0947\u0902 (<span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">0\\le r&lt;|a|<\/span><\/span>) \u0924\u0925\u093e \u0905\u0938\u094d\u092a\u0937\u094d\u091f\u0924\u093e\u0913\u0902 \u0938\u0947 \u092c\u091a\u0928\u0947 \u0915\u0947 \u0932\u093f\u090f \u0909\u0928\u0915\u093e \u0909\u0926\u094d\u0926\u0947\u0936\u094d\u092f \u0936\u093e\u092e\u093f\u0932 \u0939\u0948\u0964<\/li>\n<li><strong>\u0932\u093e\u0917\u0942 \u0915\u0930\u0928\u0947<\/strong> \u0915\u0947 \u0932\u093f\u090f \u092f\u0942\u0915\u094d\u0932\u093f\u0921\u0940\u092f \u0935\u093f\u0918\u091f\u0928 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">b=qa+r<\/span><\/span> \u0915\u093e, \u0924\u093e\u0915\u093f \u0920\u094b\u0938 \u0909\u0926\u093e\u0939\u0930\u0923\u094b\u0902 \u092e\u0947\u0902 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">q<\/span><\/span> \u0914\u0930 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">r<\/span><\/span> \u0928\u093f\u0930\u094d\u0927\u093e\u0930\u093f\u0924 \u0915\u093f\u090f \u091c\u093e \u0938\u0915\u0947\u0902 \u0914\u0930 \u0936\u0947\u0937 \u0915\u0940 \u0938\u0940\u092e\u093e \u0915\u0940 \u092a\u0941\u0937\u094d\u091f\u093f \u0915\u0940 \u091c\u093e \u0938\u0915\u0947\u0964<\/li>\n<li><strong>\u0935\u093f\u0936\u094d\u0932\u0947\u0937\u0923 \u0915\u0930\u0928\u0947<\/strong> \u0915\u0947 \u0932\u093f\u090f \u092d\u093e\u091c\u094d\u092f \u0914\u0930 \u092d\u093e\u091c\u0915 \u0915\u0947 \u091a\u093f\u0928\u094d\u0939 \u0915\u0947 \u0905\u0928\u0941\u0938\u093e\u0930 \u092e\u093e\u092e\u0932\u094b\u0902 \u0915\u0947 \u0909\u092a\u091a\u093e\u0930 \u0915\u093e, \u092f\u0939 \u0914\u091a\u093f\u0924\u094d\u092f \u092a\u094d\u0930\u0938\u094d\u0924\u0941\u0924 \u0915\u0930\u0924\u0947 \u0939\u0941\u090f \u0915\u093f \u092f\u0942\u0915\u094d\u0932\u093f\u0921\u0940\u092f \u092a\u0930\u0902\u092a\u0930\u093e \u0936\u0947\u0937 \u0915\u094b \u0917\u0948\u0930-\u090b\u0923\u093e\u0924\u094d\u092e\u0915 \u0915\u094d\u092f\u094b\u0902 \u092c\u0928\u093e\u090f \u0930\u0916\u0924\u0940 \u0939\u0948\u0964<\/li>\n<li><strong>\u0928\u093f\u0937\u094d\u092a\u093e\u0926\u093f\u0924 \u0915\u0930\u0928\u0947<\/strong> \u0915\u0947 \u0932\u093f\u090f \u0932\u0902\u092c\u0947 \u0935\u093f\u092d\u093e\u091c\u0928 \u0915\u0947 \u090f\u0932\u094d\u0917\u094b\u0930\u093f\u0926\u094d\u092e \u0915\u094b, \u0938\u094d\u0925\u093e\u0928\u093f\u0915 \u0928\u093f\u0930\u0942\u092a\u0923 \u092a\u0930 \u0906\u0927\u093e\u0930\u093f\u0924 \u090f\u0915 \u092f\u093e\u0902\u0924\u094d\u0930\u093f\u0915 \u092a\u094d\u0930\u0915\u094d\u0930\u093f\u092f\u093e \u0915\u0947 \u0930\u0942\u092a \u092e\u0947\u0902, \u0924\u093e\u0915\u093f <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">q<\/span><\/span> \u0914\u0930 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">r<\/span><\/span> \u092a\u094d\u0930\u093e\u092a\u094d\u0924 \u0915\u093f\u090f \u091c\u093e \u0938\u0915\u0947\u0902\u0964<\/li>\n<\/ol>\n<p style=\"text-align:center;\"><b><u>\u0935\u093f\u0937\u092f\u0935\u0938\u094d\u0924\u0941 \u0938\u0942\u091a\u0940<\/u>:<\/b><br \/>\n<a href=\"#1\">\u0935\u093f\u092d\u093e\u091c\u0928 \u0914\u0930 \u0935\u093f\u092d\u093e\u091c\u094d\u092f\u0924\u093e<\/a><br \/>\n<a href=\"#2\">\u092f\u0942\u0915\u094d\u0932\u093f\u0921\u0940\u092f \u0935\u093f\u092d\u093e\u091c\u0928 \u0915\u093e \u092a\u094d\u0930\u092e\u0947\u092f<\/a><br \/>\n<a href=\"#3\">\u092f\u0942\u0915\u094d\u0932\u093f\u0921\u0940\u092f \u0935\u093f\u092d\u093e\u091c\u0928 \u0915\u093e \u092a\u094d\u0930\u092e\u093e\u0923<\/a><br \/>\n<a href=\"#4\">\u092d\u093e\u0917\u092b\u0932 \u0914\u0930 \u0936\u0947\u0937 \u0915\u0940 \u0935\u094d\u092f\u093e\u0916\u094d\u092f\u093e<\/a><br \/>\n<a href=\"#5\">\u0932\u0902\u092c\u093e \u0935\u093f\u092d\u093e\u091c\u0928 \u090f\u0932\u094d\u0917\u094b\u0930\u093f\u0926\u094d\u092e<\/a><br \/>\n<a href=\"#6\">\u0928\u093f\u0937\u094d\u0915\u0930\u094d\u0937<\/a><br \/>\n<a href=\"#7\">\u092a\u094d\u0930\u0938\u094d\u0924\u093e\u0935\u093f\u0924 \u0914\u0930 \u0939\u0932 \u0915\u093f\u090f \u0917\u090f \u0905\u092d\u094d\u092f\u093e\u0938<\/a>\n<\/p>\n<p><a name=\"1\"><\/a><\/p>\n<h2>\u0935\u093f\u092d\u093e\u091c\u0928 \u0914\u0930 \u0935\u093f\u092d\u093e\u091c\u094d\u092f\u0924\u093e<\/h2>\n<p><center><iframe class=\"lazyload\" width=\"560\" height=\"315\" data-src=\"https:\/\/www.youtube.com\/embed\/nlER6VzrGwA?si=79gpsAzwc7wcWEVn\" title=\"YouTube video player\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture; web-share\" referrerpolicy=\"strict-origin-when-cross-origin\" allowfullscreen><\/iframe><\/center><\/p>\n<p>\u0905\u0902\u0915\u0917\u0923\u093f\u0924 \u092e\u0947\u0902, \u0935\u093f\u092d\u093e\u091c\u094d\u092f\u0924\u093e \u00ab\u0938\u091f\u0940\u0915\u00bb \u0938\u094d\u0925\u093f\u0924\u093f \u0915\u093e \u0935\u0930\u094d\u0923\u0928 \u0915\u0930\u0924\u0940 \u0939\u0948: <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">a\\mid b<\/span><\/span> \u0915\u093e \u0905\u0930\u094d\u0925 \u0939\u0948 \u0915\u093f <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">b<\/span><\/span> \u0915\u094b \u0920\u0940\u0915-\u0920\u0940\u0915 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">a<\/span><\/span> \u0915\u0947 \u0917\u0941\u0923\u091c \u0915\u0947 \u0930\u0942\u092a \u092e\u0947\u0902 \u0932\u093f\u0916\u093e \u091c\u093e \u0938\u0915\u0924\u093e \u0939\u0948\u0964 \u0924\u0925\u093e\u092a\u093f, \u092f\u0926\u094d\u092f\u092a\u093f \u0915\u093f\u0938\u0940 \u092d\u0940 \u0926\u094b \u092a\u0942\u0930\u094d\u0923\u093e\u0902\u0915\u094b\u0902 \u0915\u0947 \u092c\u0940\u091a \u0939\u092e\u0947\u0936\u093e \u0935\u093f\u092d\u093e\u091c\u094d\u092f\u0924\u093e \u0928\u0939\u0940\u0902 \u0939\u094b\u0924\u0940, \u092b\u093f\u0930 \u092d\u0940 \u0939\u092e \u092f\u0939 \u092a\u0942\u091b \u0938\u0915\u0924\u0947 \u0939\u0948\u0902 \u0915\u093f \u00ab\u090f\u0915 \u0938\u0902\u0916\u094d\u092f\u093e \u0926\u0942\u0938\u0930\u0940 \u092e\u0947\u0902 \u0915\u093f\u0924\u0928\u0940 \u092c\u093e\u0930 \u0938\u092e\u093e\u0939\u093f\u0924 \u0939\u094b\u0924\u0940 \u0939\u0948 \u0914\u0930, \u092f\u0926\u093f \u0935\u0939 \u0920\u0940\u0915-\u0920\u0940\u0915 \u0928 \u0939\u094b, \u0924\u094b \u0915\u094d\u092f\u093e \u0936\u0947\u0937 \u092c\u091a\u0924\u093e \u0939\u0948\u00bb\u0964 \u092f\u0939\u0940 \u0935\u0939 \u0938\u0902\u0926\u0930\u094d\u092d \u0939\u0948 \u091c\u093f\u0938\u092e\u0947\u0902 <strong>\u0935\u093f\u092d\u093e\u091c\u0928 \u0915\u093e \u090f\u0932\u094d\u0917\u094b\u0930\u093f\u0926\u094d\u092e<\/strong> \u0909\u0924\u094d\u092a\u0928\u094d\u0928 \u0939\u094b\u0924\u093e \u0939\u0948, \u091c\u094b \u092f\u0939 \u0938\u0941\u0928\u093f\u0936\u094d\u091a\u093f\u0924 \u0915\u0930\u0924\u093e \u0939\u0948 \u0915\u093f \u0915\u094b\u0908 \u092d\u0940 \u092a\u0942\u0930\u094d\u0923\u093e\u0902\u0915 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">b<\/span><\/span> \u0915\u094b <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">a<\/span><\/span> \u0915\u0947 \u0917\u0941\u0923\u091c \u0915\u0947 \u0938\u093e\u0925 \u090f\u0915 \u00ab\u0936\u0947\u0937\u00bb \u091c\u094b\u0921\u093c\u0915\u0930 \u0932\u093f\u0916\u093e \u091c\u093e \u0938\u0915\u0924\u093e \u0939\u0948\u0964<\/p>\n<p>\u0909\u0926\u093e\u0939\u0930\u0923 \u0915\u0947 \u0930\u0942\u092a \u092e\u0947\u0902, <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">a=3<\/span><\/span> \u0914\u0930 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">b=16<\/span><\/span> \u092a\u0930 \u0935\u093f\u091a\u093e\u0930 \u0915\u0930\u0947\u0902\u0964 \u092f\u0939 \u0938\u094d\u092a\u0937\u094d\u091f \u0939\u0948 \u0915\u093f 3, 16 \u0915\u094b \u0935\u093f\u092d\u093e\u091c\u093f\u0924 \u0928\u0939\u0940\u0902 \u0915\u0930\u0924\u093e\u0964 \u092b\u093f\u0930 \u092d\u0940, \u0935\u093f\u092d\u093e\u091c\u0928 \u0915\u0940 \u0915\u094d\u0930\u093f\u092f\u093e \u0915\u0947 \u0932\u093f\u090f \u090f\u0915 \u092d\u093e\u0917\u092b\u0932 \u0914\u0930 \u090f\u0915 \u0936\u0947\u0937 \u092a\u094d\u0930\u093e\u092a\u094d\u0924 \u0915\u093f\u092f\u093e \u091c\u093e \u0938\u0915\u0924\u093e \u0939\u0948, \u0915\u094d\u092f\u094b\u0902\u0915\u093f<\/p>\n<p style=\"text-align:center;\"><span class=\"katex-eq\" data-katex-display=\"false\">16 = 5\\cdot 3 + 1<\/span>\n<figure id=\"attachment_35775\" aria-describedby=\"caption-attachment-35775\" style=\"width: 1492px\" class=\"wp-caption aligncenter\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"http:\/\/toposuranos.com\/material\/wp-content\/uploads\/2025\/12\/division16por3.jpg\" alt=\"Un grupo de 16 cajas han sido separadas en grupos de a 3, como resultado se obtienen 5 grupos de cajas y sobra 1\" width=\"1492\" height=\"230\" class=\"size-full wp-image-35775 lazyload\" \/><figcaption id=\"caption-attachment-35775\" class=\"wp-caption-text\"><noscript><img decoding=\"async\" src=\"http:\/\/toposuranos.com\/material\/wp-content\/uploads\/2025\/12\/division16por3.jpg\" alt=\"Un grupo de 16 cajas han sido separadas en grupos de a 3, como resultado se obtienen 5 grupos de cajas y sobra 1\" width=\"1492\" height=\"230\" class=\"size-full wp-image-35775 lazyload\" srcset=\"https:\/\/toposuranos.com\/material\/wp-content\/uploads\/2025\/12\/division16por3.jpg 1492w, https:\/\/toposuranos.com\/material\/wp-content\/uploads\/2025\/12\/division16por3-300x46.jpg 300w, https:\/\/toposuranos.com\/material\/wp-content\/uploads\/2025\/12\/division16por3-1024x158.jpg 1024w, https:\/\/toposuranos.com\/material\/wp-content\/uploads\/2025\/12\/division16por3-768x118.jpg 768w\" sizes=\"(max-width: 1492px) 100vw, 1492px\" \/><\/noscript> 16 \u092c\u0915\u094d\u0938\u094b\u0902 \u0915\u0947 \u090f\u0915 \u0938\u092e\u0942\u0939 \u0915\u094b 3-3 \u0915\u0947 \u0938\u092e\u0942\u0939\u094b\u0902 \u092e\u0947\u0902 \u0935\u093f\u092d\u093e\u091c\u093f\u0924 \u0915\u093f\u092f\u093e \u0917\u092f\u093e \u0939\u0948; \u092a\u0930\u093f\u0923\u093e\u092e\u0938\u094d\u0935\u0930\u0942\u092a 5 \u092c\u0915\u094d\u0938\u094b\u0902 \u0915\u0947 \u0938\u092e\u0942\u0939 \u092a\u094d\u0930\u093e\u092a\u094d\u0924 \u0939\u094b\u0924\u0947 \u0939\u0948\u0902 \u0914\u0930 1 \u0936\u0947\u0937 \u092c\u091a\u0924\u093e \u0939\u0948<\/figcaption><\/figure>\n<p>\u092a\u0930\u093f\u0923\u093e\u092e\u0938\u094d\u0935\u0930\u0942\u092a, <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">b=16<\/span><\/span> \u0915\u094b <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">a=3<\/span><\/span> \u0938\u0947 \u0935\u093f\u092d\u093e\u091c\u093f\u0924 \u0915\u0930\u0928\u0947 \u092a\u0930 (\u091c\u0939\u093e\u0901 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">b<\/span><\/span> <strong>\u092d\u093e\u091c\u094d\u092f<\/strong> \u0939\u0948 \u0914\u0930 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">a<\/span><\/span> <strong>\u092d\u093e\u091c\u0915<\/strong> \u0939\u0948), \u091c\u093f\u0938\u0947 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">16\/3<\/span><\/span> \u092f\u093e <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">16\\div 3<\/span><\/span> \u0926\u094d\u0935\u093e\u0930\u093e \u0928\u093f\u0930\u0942\u092a\u093f\u0924 \u0915\u093f\u092f\u093e \u091c\u093e\u0924\u093e \u0939\u0948, <strong>\u092d\u093e\u0917\u092b\u0932<\/strong> \u0915\u0947 \u0930\u0942\u092a \u092e\u0947\u0902 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">q=5<\/span><\/span> \u0924\u0925\u093e <strong>\u0936\u0947\u0937<\/strong> \u0915\u0947 \u0930\u0942\u092a \u092e\u0947\u0902 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">r=1<\/span><\/span> \u092a\u094d\u0930\u093e\u092a\u094d\u0924 \u0939\u094b\u0924\u093e \u0939\u0948\u0964 \u0938\u093e\u092e\u093e\u0928\u094d\u092f \u0930\u0942\u092a \u092e\u0947\u0902, <em>\u0935\u093f\u092d\u093e\u091c\u0928 \u0915\u093e \u090f\u0932\u094d\u0917\u094b\u0930\u093f\u0926\u094d\u092e<\/em> \u092f\u0939 \u0915\u0925\u0928 \u0915\u0930\u0924\u093e \u0939\u0948 \u0915\u093f \u0915\u093f\u0938\u0940 \u092d\u0940 \u092a\u0942\u0930\u094d\u0923\u093e\u0902\u0915 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">a<\/span><\/span> (\u092d\u093e\u091c\u0915) \u0914\u0930 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">b<\/span><\/span> (\u092d\u093e\u091c\u094d\u092f) \u0915\u0947 \u0932\u093f\u090f, \u091c\u0939\u093e\u0901 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">a\\neq 0<\/span><\/span>, \u0905\u0926\u094d\u0935\u093f\u0924\u0940\u092f \u092a\u0942\u0930\u094d\u0923\u093e\u0902\u0915 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">q<\/span><\/span> \u0914\u0930 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">r<\/span><\/span> \u0905\u0938\u094d\u0924\u093f\u0924\u094d\u0935 \u092e\u0947\u0902 \u0939\u094b\u0924\u0947 \u0939\u0948\u0902, \u0910\u0938\u0947 \u0915\u093f<\/p>\n<p style=\"text-align:center;\"><span class=\"katex-eq\" data-katex-display=\"false\">b=qa+r,\\qquad 0\\le r&lt;|a|<\/span>\n<p>\u0907\u0938 \u0909\u0926\u093e\u0939\u0930\u0923 \u092e\u0947\u0902, <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">16=3\\cdot 5+1<\/span><\/span> \u0939\u0948, \u0914\u0930 \u0936\u0930\u094d\u0924 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">0\\le r&lt;|a|<\/span><\/span> \u0907\u0938\u0932\u093f\u090f \u092a\u0942\u0930\u0940 \u0939\u094b\u0924\u0940 \u0939\u0948 \u0915\u094d\u092f\u094b\u0902\u0915\u093f <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">0\\le 1&lt;3<\/span><\/span>\u0964 \u092f\u0939 \u0938\u0942\u0924\u094d\u0930\u0940\u0915\u0930\u0923 \u0924\u092c \u0905\u0938\u094d\u092a\u0937\u094d\u091f\u0924\u093e\u0913\u0902 \u0938\u0947 \u092c\u091a\u093e\u0924\u093e \u0939\u0948 \u091c\u092c \u092d\u093e\u091c\u0915 (\u092f\u093e \u092d\u093e\u091c\u094d\u092f) \u090b\u0923\u093e\u0924\u094d\u092e\u0915 \u0939\u094b \u0938\u0915\u0924\u093e \u0939\u0948, \u0914\u0930 \u092f\u0939 \u0938\u0941\u0928\u093f\u0936\u094d\u091a\u093f\u0924 \u0915\u0930\u0924\u093e \u0939\u0948 \u0915\u093f \u0936\u0947\u0937 \u0939\u092e\u0947\u0936\u093e \u0917\u0948\u0930-\u090b\u0923\u093e\u0924\u094d\u092e\u0915 \u0939\u094b \u0924\u0925\u093e \u092d\u093e\u091c\u0915 \u0915\u0947 \u092a\u0930\u093f\u092e\u093e\u0923 \u0938\u0947 \u0938\u0916\u094d\u0924\u0940 \u0938\u0947 \u091b\u094b\u091f\u093e \u0939\u094b\u0964<\/p>\n<p><a name=\"2\"><\/a><\/p>\n<h2>\u092f\u0942\u0915\u094d\u0932\u093f\u0921\u0940\u092f \u0935\u093f\u092d\u093e\u091c\u0928 \u0915\u093e \u092a\u094d\u0930\u092e\u0947\u092f<\/h2>\n<p>\u0935\u093f\u092d\u093e\u091c\u0928 \u0915\u0947 \u090f\u0932\u094d\u0917\u094b\u0930\u093f\u0926\u094d\u092e \u0915\u094b \u0932\u093e\u0917\u0942 \u0915\u0930\u0928\u0947 \u0915\u093e \u092a\u0930\u093f\u0923\u093e\u092e \u0935\u0939\u0940 \u0939\u0948 \u091c\u093f\u0938\u0947 <strong>\u092f\u0942\u0915\u094d\u0932\u093f\u0921\u0940\u092f \u0935\u093f\u092d\u093e\u091c\u0928<\/strong> \u0915\u0939\u093e \u091c\u093e\u0924\u093e \u0939\u0948, \u0914\u0930 \u092f\u0939 \u0928\u093f\u092e\u094d\u0928\u0932\u093f\u0916\u093f\u0924 \u092a\u0930\u093f\u0923\u093e\u092e \u092a\u0930 \u0906\u0927\u093e\u0930\u093f\u0924 \u0939\u0948\u0964<\/p>\n<p><b>\u092a\u094d\u0930\u092e\u0947\u092f:<\/b> \u092e\u093e\u0928 \u0932\u0947\u0902 \u0915\u093f <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">a,b\\in\\mathbb{Z}<\/span><\/span> \u0939\u0948\u0902 \u0914\u0930 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">a\\neq 0<\/span><\/span>\u0964 \u0924\u092c \u0905\u0926\u094d\u0935\u093f\u0924\u0940\u092f <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">q,r\\in\\mathbb{Z}<\/span><\/span> \u0905\u0938\u094d\u0924\u093f\u0924\u094d\u0935 \u092e\u0947\u0902 \u0939\u094b\u0924\u0947 \u0939\u0948\u0902, \u0910\u0938\u0947 \u0915\u093f<\/p>\n<p style=\"text-align:center;\" dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\nb=qa+r,\\qquad 0\\le r&lt;|a|.\n\n<\/span>\n<p>\u092a\u0942\u0930\u094d\u0923\u093e\u0902\u0915 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">q<\/span><\/span> \u0915\u094b <strong>\u092d\u093e\u0917\u092b\u0932<\/strong> \u0914\u0930 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">r<\/span><\/span> \u0915\u094b <strong>\u0936\u0947\u0937<\/strong> \u0915\u0939\u093e \u091c\u093e\u0924\u093e \u0939\u0948, \u091c\u094b <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">b<\/span><\/span> \u0915\u094b <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">a<\/span><\/span> \u0938\u0947 \u0935\u093f\u092d\u093e\u091c\u093f\u0924 \u0915\u0930\u0928\u0947 \u092a\u0930 \u092a\u094d\u0930\u093e\u092a\u094d\u0924 \u0939\u094b\u0924\u0947 \u0939\u0948\u0902\u0964<\/p>\n<p><a name=\"3\"><\/a><\/p>\n<h2>\u092f\u0942\u0915\u094d\u0932\u093f\u0921\u0940\u092f \u0935\u093f\u092d\u093e\u091c\u0928 \u0915\u093e \u092a\u094d\u0930\u092e\u093e\u0923<\/h2>\n<p>\u092f\u0939 \u092a\u094d\u0930\u092e\u093e\u0923 \u0926\u094b \u092d\u093e\u0917\u094b\u0902 \u092e\u0947\u0902 \u0935\u093f\u092d\u093e\u091c\u093f\u0924 \u0939\u0948: \u092a\u0939\u0932\u0947 \u092f\u0939 \u0926\u093f\u0916\u093e\u092f\u093e \u091c\u093e\u0924\u093e \u0939\u0948 \u0915\u093f \u092d\u093e\u0917\u092b\u0932 \u0914\u0930 \u0936\u0947\u0937 \u0905\u0938\u094d\u0924\u093f\u0924\u094d\u0935 \u092e\u0947\u0902 \u0939\u0948\u0902; \u0914\u0930 \u092b\u093f\u0930, \u092f\u0939 \u092e\u093e\u0928\u0924\u0947 \u0939\u0941\u090f \u0915\u093f \u0935\u0947 \u0905\u0938\u094d\u0924\u093f\u0924\u094d\u0935 \u092e\u0947\u0902 \u0939\u0948\u0902, \u092f\u0939 \u0938\u093f\u0926\u094d\u0927 \u0915\u093f\u092f\u093e \u091c\u093e\u0924\u093e \u0939\u0948 \u0915\u093f \u0935\u0947 \u0905\u0926\u094d\u0935\u093f\u0924\u0940\u092f \u0939\u0948\u0902\u0964<\/p>\n<h3>\u0905\u0938\u094d\u0924\u093f\u0924\u094d\u0935<\/h3>\n<p>\u092e\u093e\u0928 \u0932\u0947\u0902 \u0915\u093f <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">a,b\\in\\mathbb{Z}<\/span><\/span> \u0939\u0948\u0902 \u0914\u0930 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">a\\neq 0<\/span><\/span>\u0964 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">d=|a|<\/span><\/span> \u092a\u0930\u093f\u092d\u093e\u0937\u093f\u0924 \u0915\u0930\u0947\u0902, \u0924\u093e\u0915\u093f <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">d&gt;0<\/span><\/span> \u0939\u094b\u0964 \u092a\u0939\u0932\u0947 \u0939\u092e <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">b\\ge 0<\/span><\/span> \u0915\u093e \u092e\u093e\u092e\u0932\u093e \u0938\u093f\u0926\u094d\u0927 \u0915\u0930\u0947\u0902\u0917\u0947: \u0939\u092e \u092f\u0939 \u0926\u093f\u0916\u093e\u090f\u0901\u0917\u0947 \u0915\u093f \u0910\u0938\u0947 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">q,r\\in\\mathbb{Z}<\/span><\/span> \u0905\u0938\u094d\u0924\u093f\u0924\u094d\u0935 \u092e\u0947\u0902 \u0939\u0948\u0902 \u0915\u093f <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">b=dq+r<\/span><\/span> \u0924\u0925\u093e <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">0\\le r&lt;d<\/span><\/span>\u0964 \u0907\u0938\u0915\u0947 \u092c\u093e\u0926 \u0939\u092e <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">b&lt;0<\/span><\/span> \u0915\u0947 \u092e\u093e\u092e\u0932\u0947 \u092a\u0930 \u0935\u093f\u091a\u093e\u0930 \u0915\u0930\u0947\u0902\u0917\u0947\u0964 \u0905\u0902\u0924 \u092e\u0947\u0902, \u0939\u092e <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">d<\/span><\/span> \u0915\u094b <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">|a|<\/span><\/span> \u0938\u0947 \u092a\u094d\u0930\u0924\u093f\u0938\u094d\u0925\u093e\u092a\u093f\u0924 \u0915\u0930\u0947\u0902\u0917\u0947 \u0924\u093e\u0915\u093f \u0930\u0942\u092a <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">b=qa+r<\/span><\/span> \u092a\u094d\u0930\u093e\u092a\u094d\u0924 \u0939\u094b, \u091c\u0939\u093e\u0901 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">0\\le r&lt;|a|<\/span><\/span>\u0964<\/p>\n<p><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">b\\in\\mathbb{Z}<\/span><\/span> \u0915\u0947 \u0932\u093f\u090f \u091c\u0939\u093e\u0901 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">b\\ge 0<\/span><\/span> \u0939\u094b, \u0939\u092e \u092a\u094d\u0930\u0924\u093f\u091c\u094d\u091e\u092a\u094d\u0924\u093f <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">P(b)<\/span><\/span> \u0938\u094d\u0925\u093e\u092a\u093f\u0924 \u0915\u0930\u0924\u0947 \u0939\u0948\u0902: \u00ab\u0910\u0938\u0947 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">q,r\\in\\mathbb{Z}<\/span><\/span> \u0905\u0938\u094d\u0924\u093f\u0924\u094d\u0935 \u092e\u0947\u0902 \u0939\u0948\u0902 \u0915\u093f <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">b=dq+r<\/span><\/span> \u0924\u0925\u093e <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">0\\le r&lt;d<\/span><\/span>\u00bb\u0964 \u0939\u092e \u0906\u0917\u092e\u0928 \u0926\u094d\u0935\u093e\u0930\u093e \u0938\u093f\u0926\u094d\u0927 \u0915\u0930\u0947\u0902\u0917\u0947 \u0915\u093f <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">P(b)<\/span><\/span> \u092a\u094d\u0930\u0924\u094d\u092f\u0947\u0915 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">b\\ge 0<\/span><\/span> \u0915\u0947 \u0932\u093f\u090f \u0938\u0924\u094d\u092f \u0939\u0948\u0964<\/p>\n<p><strong>\u0906\u0927\u093e\u0930 \u092e\u093e\u092e\u0932\u093e:<\/strong> <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">b=0<\/span><\/span> \u0915\u0947 \u0932\u093f\u090f, <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">q=0<\/span><\/span> \u0914\u0930 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">r=0<\/span><\/span> \u0932\u0947\u0928\u0947 \u092a\u0930 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">0=d\\cdot 0+0<\/span><\/span> \u0924\u0925\u093e <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">0\\le 0&lt;d<\/span><\/span> \u092a\u094d\u0930\u093e\u092a\u094d\u0924 \u0939\u094b\u0924\u093e \u0939\u0948\u0964 \u0905\u0924\u0903 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">P(0)<\/span><\/span> \u0938\u0924\u094d\u092f \u0939\u0948\u0964<\/p>\n<p><strong>\u0906\u0917\u092e\u0928 \u091a\u0930\u0923:<\/strong> \u092e\u093e\u0928 \u0932\u0947\u0902 \u0915\u093f <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">k\\ge 0<\/span><\/span> \u0939\u0948 \u0914\u0930 \u092f\u0939 \u092e\u093e\u0928 \u0932\u0947\u0902 \u0915\u093f <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">P(k)<\/span><\/span> \u0938\u0924\u094d\u092f \u0939\u0948\u0964 \u0924\u092c \u0910\u0938\u0947 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">q,r\\in\\mathbb{Z}<\/span><\/span> \u0905\u0938\u094d\u0924\u093f\u0924\u094d\u0935 \u092e\u0947\u0902 \u0939\u0948\u0902 \u0915\u093f<\/p>\n<p style=\"text-align:center;\" dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\nk=dq+r,\\qquad 0\\le r&lt;d.\n\n<\/span>\n<p>\u0926\u094b\u0928\u094b\u0902 \u092a\u0915\u094d\u0937\u094b\u0902 \u092e\u0947\u0902 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">1<\/span><\/span> \u091c\u094b\u0921\u093c\u0928\u0947 \u092a\u0930 \u092a\u094d\u0930\u093e\u092a\u094d\u0924 \u0939\u094b\u0924\u093e \u0939\u0948<\/p>\n<p style=\"text-align:center;\" dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\nk+1=dq+(r+1).\n\n<\/span>\n<p>\u0907\u0938\u0915\u0947 \u0905\u0924\u093f\u0930\u093f\u0915\u094d\u0924, <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">0\\le r&lt;d<\/span><\/span> \u0938\u0947 \u092f\u0939 \u0928\u093f\u0937\u094d\u0915\u0930\u094d\u0937 \u0928\u093f\u0915\u0932\u0924\u093e \u0939\u0948 \u0915\u093f <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">r+1\\le d<\/span><\/span>\u0964 \u092a\u0930\u093f\u0923\u093e\u092e\u0938\u094d\u0935\u0930\u0942\u092a, \u0915\u0947\u0935\u0932 \u0926\u094b \u0938\u094d\u0925\u093f\u0924\u093f\u092f\u093e\u0901 \u0938\u0902\u092d\u0935 \u0939\u0948\u0902: <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">r+1&lt;d<\/span><\/span> \u092f\u093e <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">r+1=d<\/span><\/span>\u0964<\/p>\n<p><b>\u0938\u094d\u0925\u093f\u0924\u093f 1:<\/b> \u092f\u0926\u093f <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">r+1&lt;d<\/span><\/span> \u0939\u094b, \u0924\u094b \u0939\u092e <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">q&#039;=q<\/span><\/span> \u0914\u0930 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">r&#039;=r+1<\/span><\/span> \u092a\u0930\u093f\u092d\u093e\u0937\u093f\u0924 \u0915\u0930\u0924\u0947 \u0939\u0948\u0902\u0964 \u0924\u092c<\/p>\n<p style=\"text-align:center;\" dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\nk+1=dq&#039;+r&#039;,\\qquad 0\\le r&#039;&lt;d.\n\n<\/span>\n<p><b>\u0938\u094d\u0925\u093f\u0924\u093f 2:<\/b> \u092f\u0926\u093f <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">r+1=d<\/span><\/span> \u0939\u094b, \u0924\u094b <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">k+1=dq+d=d(q+1)+0<\/span><\/span>\u0964 \u0939\u092e <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">q&#039;=q+1<\/span><\/span> \u0914\u0930 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">r&#039;=0<\/span><\/span> \u092a\u0930\u093f\u092d\u093e\u0937\u093f\u0924 \u0915\u0930\u0924\u0947 \u0939\u0948\u0902, \u0914\u0930 \u0924\u092c<\/p>\n<p style=\"text-align:center;\" dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\nk+1=dq&#039;+r&#039;,\\qquad 0\\le r&#039;&lt;d.\n\n<\/span>\n<p>\u0926\u094b\u0928\u094b\u0902 \u0938\u094d\u0925\u093f\u0924\u093f\u092f\u094b\u0902 \u092e\u0947\u0902 \u0939\u092e\u0928\u0947 \u0910\u0938\u0947 \u092a\u0942\u0930\u094d\u0923\u093e\u0902\u0915 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">q&#039;,r&#039;<\/span><\/span> \u0928\u093f\u0930\u094d\u092e\u093f\u0924 \u0915\u093f\u090f \u0939\u0948\u0902 \u0915\u093f <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">k+1=dq&#039;+r&#039;<\/span><\/span> \u0924\u0925\u093e <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">0\\le r&#039;&lt;d<\/span><\/span>\u0964 \u0905\u0924\u0903 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">P(k+1)<\/span><\/span> \u0938\u0924\u094d\u092f \u0939\u0948\u0964 \u0939\u092e \u0906\u0917\u092e\u0928 \u0926\u094d\u0935\u093e\u0930\u093e \u0928\u093f\u0937\u094d\u0915\u0930\u094d\u0937 \u0928\u093f\u0915\u093e\u0932\u0924\u0947 \u0939\u0948\u0902 \u0915\u093f <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">P(b)<\/span><\/span> \u092a\u094d\u0930\u0924\u094d\u092f\u0947\u0915 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">b\\ge 0<\/span><\/span> \u0915\u0947 \u0932\u093f\u090f \u092e\u093e\u0928\u094d\u092f \u0939\u0948\u0964<\/p>\n<p>\u0905\u092c <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">b&lt;0<\/span><\/span> \u0915\u0947 \u092e\u093e\u092e\u0932\u0947 \u092a\u0930 \u0935\u093f\u091a\u093e\u0930 \u0915\u0930\u0947\u0902\u0964 \u0924\u092c <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">-b&gt;0<\/span><\/span> \u0939\u094b\u0924\u093e \u0939\u0948\u0964 \u0909\u092a\u0930\u094d\u092f\u0941\u0915\u094d\u0924 \u092a\u0930\u093f\u0923\u093e\u092e \u0915\u094b <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">-b<\/span><\/span> \u092a\u0930 \u0932\u093e\u0917\u0942 \u0915\u0930\u0928\u0947 \u0938\u0947 \u0910\u0938\u0947 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">q,r\\in\\mathbb{Z}<\/span><\/span> \u0905\u0938\u094d\u0924\u093f\u0924\u094d\u0935 \u092e\u0947\u0902 \u0939\u0948\u0902 \u0915\u093f<\/p>\n<p style=\"text-align:center;\" dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\n-b=dq+r,\\qquad 0\\le r&lt;d.\n\n<\/span>\n<p><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">-1<\/span><\/span> \u0938\u0947 \u0917\u0941\u0923\u093e \u0915\u0930\u0928\u0947 \u092a\u0930 \u092a\u094d\u0930\u093e\u092a\u094d\u0924 \u0939\u094b\u0924\u093e \u0939\u0948<\/p>\n<p style=\"text-align:center;\" dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\nb=-dq-r.\n\n<\/span>\n<p>\u092f\u0926\u093f <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">r=0<\/span><\/span> \u0939\u094b, \u0924\u094b <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">q_1=-q<\/span><\/span> \u0914\u0930 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">r_1=0<\/span><\/span> \u0932\u0947\u0928\u093e \u092a\u0930\u094d\u092f\u093e\u092a\u094d\u0924 \u0939\u0948, \u091c\u093f\u0938\u0938\u0947 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">b=dq_1+r_1<\/span><\/span> \u0924\u0925\u093e <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">0\\le r_1&lt;d<\/span><\/span> \u092a\u094d\u0930\u093e\u092a\u094d\u0924 \u0939\u094b\u0924\u093e \u0939\u0948\u0964<\/p>\n<p>\u092f\u0926\u093f <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">r&gt;0<\/span><\/span> \u0939\u094b, \u0924\u094b \u0939\u092e <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">q_1=-q-1<\/span><\/span> \u0914\u0930 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">r_1=d-r<\/span><\/span> \u092a\u0930\u093f\u092d\u093e\u0937\u093f\u0924 \u0915\u0930\u0924\u0947 \u0939\u0948\u0902\u0964 \u091a\u0942\u0901\u0915\u093f <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">0&lt;r&lt;d<\/span><\/span>, \u0907\u0938\u0932\u093f\u090f <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">0&lt;d-r&lt;d<\/span><\/span> \u0939\u094b\u0924\u093e \u0939\u0948, \u0905\u0930\u094d\u0925\u093e\u0924\u094d <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">0\\le r_1&lt;d<\/span><\/span>\u0964 \u0907\u0938\u0915\u0947 \u0905\u0924\u093f\u0930\u093f\u0915\u094d\u0924,<\/p>\n<p style=\"text-align:center;\" dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\ndq_1+r_1=d(-q-1)+(d-r)=-dq-d+d-r=-dq-r=b.\n\n<\/span>\n<p>\u092a\u0930\u093f\u0923\u093e\u092e\u0938\u094d\u0935\u0930\u0942\u092a, \u092a\u094d\u0930\u0924\u094d\u092f\u0947\u0915 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">b\\in\\mathbb{Z}<\/span><\/span> \u0915\u0947 \u0932\u093f\u090f \u0910\u0938\u0947 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">q_1,r_1\\in\\mathbb{Z}<\/span><\/span> \u0905\u0938\u094d\u0924\u093f\u0924\u094d\u0935 \u092e\u0947\u0902 \u0939\u0948\u0902 \u0915\u093f <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">b=dq_1+r_1<\/span><\/span> \u0924\u0925\u093e <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">0\\le r_1&lt;d<\/span><\/span>\u0964<\/p>\n<p>\u0905\u0902\u0924\u0924\u0903, \u0938\u094d\u092e\u0930\u0923 \u0915\u0930\u0947\u0902 \u0915\u093f <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">d=|a|<\/span><\/span> \u0939\u0948\u0964 \u092f\u0926\u093f <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">a&gt;0<\/span><\/span>, \u0924\u094b <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">d=a<\/span><\/span> \u0914\u0930 \u0938\u092e\u093e\u0928\u0924\u093e <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">b=dq_1+r_1<\/span><\/span> \u0915\u094b <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">b=aq_1+r_1<\/span><\/span> \u0915\u0947 \u0930\u0942\u092a \u092e\u0947\u0902 \u0932\u093f\u0916\u093e \u091c\u093e\u0924\u093e \u0939\u0948, \u091c\u0939\u093e\u0901 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">0\\le r_1&lt;|a|<\/span><\/span>\u0964<\/p>\n<p>\u092f\u0926\u093f <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">a&lt;0<\/span><\/span>, \u0924\u094b <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">d=-a<\/span><\/span> \u0914\u0930 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">b=dq_1+r_1=(-a)q_1+r_1=a(-q_1)+r_1<\/span><\/span>\u0964 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">q=-q_1<\/span><\/span> \u0914\u0930 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">r=r_1<\/span><\/span> \u092a\u0930\u093f\u092d\u093e\u0937\u093f\u0924 \u0915\u0930\u0928\u0947 \u092a\u0930 \u092a\u094d\u0930\u093e\u092a\u094d\u0924 \u0939\u094b\u0924\u093e \u0939\u0948<\/p>\n<p style=\"text-align:center;\" dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\nb=qa+r,\\qquad 0\\le r&lt;|a|.\n\n<\/span>\n<p>\u0907\u0938 \u092a\u094d\u0930\u0915\u093e\u0930, \u0915\u093f\u0938\u0940 \u092d\u0940 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">a,b\\in\\mathbb{Z}<\/span><\/span> \u0915\u0947 \u0932\u093f\u090f, \u091c\u0939\u093e\u0901 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">a\\neq 0<\/span><\/span>, <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">q<\/span><\/span> \u0914\u0930 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">r<\/span><\/span> \u0915\u0947 \u0905\u0938\u094d\u0924\u093f\u0924\u094d\u0935 \u0915\u093e \u092a\u094d\u0930\u092e\u093e\u0923 \u092a\u0942\u0930\u094d\u0923 \u0939\u094b \u091c\u093e\u0924\u093e \u0939\u0948\u0964<\/p>\n<h3>\u090f\u0915\u093e\u0924\u094d\u092e\u0915\u0924\u093e<\/h3>\n<p>\u092e\u093e\u0928 \u0932\u0947\u0902 \u0915\u093f \u0910\u0938\u0947 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">q,q&#039;,r,r&#039;\\in\\mathbb{Z}<\/span><\/span> \u0905\u0938\u094d\u0924\u093f\u0924\u094d\u0935 \u092e\u0947\u0902 \u0939\u0948\u0902 \u0915\u093f<\/p>\n<p style=\"text-align:center;\" dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\nb=qa+r=q&#039;a+r&#039;,\\qquad 0\\le r,r&#039;&lt;|a|.\n\n<\/span>\n<p>\u0926\u094b\u0928\u094b\u0902 \u0935\u094d\u092f\u0902\u091c\u0915\u094b\u0902 \u0915\u094b \u0918\u091f\u093e\u0928\u0947 \u092a\u0930 \u092a\u094d\u0930\u093e\u092a\u094d\u0924 \u0939\u094b\u0924\u093e \u0939\u0948<\/p>\n<p style=\"text-align:center;\" dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\na(q-q&#039;)=r&#039;-r.\n\n<\/span>\n<p>\u091a\u0942\u0901\u0915\u093f <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">0\\le r,r&#039;&lt;|a|<\/span><\/span>, \u0907\u0938\u0932\u093f\u090f <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">|r&#039;-r|&lt;|a|<\/span><\/span> \u0939\u094b\u0924\u093e \u0939\u0948\u0964 \u0926\u0942\u0938\u0930\u0940 \u0913\u0930, \u092c\u093e\u092f\u093e\u0901 \u092a\u0915\u094d\u0937 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">a<\/span><\/span> \u0915\u093e \u0917\u0941\u0923\u091c \u0939\u0948, \u0914\u0930 \u0907\u0938\u0932\u093f\u090f <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">|a|<\/span><\/span> \u0915\u093e \u092d\u0940 \u0917\u0941\u0923\u091c \u0939\u0948\u0964 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">|a|<\/span><\/span> \u0915\u093e \u090f\u0915\u092e\u093e\u0924\u094d\u0930 \u092a\u0942\u0930\u094d\u0923\u093e\u0902\u0915 \u0917\u0941\u0923\u091c \u091c\u093f\u0938\u0915\u093e \u092a\u0930\u093f\u092e\u093e\u0923 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">|a|<\/span><\/span> \u0938\u0947 \u0938\u0916\u094d\u0924\u0940 \u0938\u0947 \u091b\u094b\u091f\u093e \u0939\u094b, <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">0<\/span><\/span> \u0939\u0948; \u0935\u093e\u0938\u094d\u0924\u0935 \u092e\u0947\u0902, \u092f\u0926\u093f <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">|a| m \\neq 0<\/span><\/span> \u0939\u094b \u0914\u0930 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">m\\in\\mathbb{Z}<\/span><\/span>, \u0924\u094b <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\big| |a| m \\big| \\ge |a| <\/span><\/span> \u0939\u094b\u0924\u093e \u0939\u0948\u0964 \u0905\u0924\u0903 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">r&#039;-r=0<\/span><\/span>, \u0905\u0930\u094d\u0925\u093e\u0924\u094d <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">r=r&#039;<\/span><\/span>, \u0914\u0930 \u0907\u0938\u0947 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">b=qa+r<\/span><\/span> \u092e\u0947\u0902 \u092a\u094d\u0930\u0924\u093f\u0938\u094d\u0925\u093e\u092a\u093f\u0924 \u0915\u0930\u0928\u0947 \u092a\u0930 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">q=q&#039;<\/span><\/span> \u0928\u093f\u0937\u094d\u0915\u0930\u094d\u0937 \u0928\u093f\u0915\u0932\u0924\u093e \u0939\u0948\u0964 \u0907\u0938 \u0915\u093e\u0930\u0923 \u092f\u0939 \u0935\u093f\u0918\u091f\u0928 \u090f\u0915\u093e\u0924\u094d\u092e\u0915 \u0939\u0948\u0964<\/p>\n<p><a name=\"4\"><\/a><\/p>\n<h2>\u092d\u093e\u0917\u092b\u0932 \u0914\u0930 \u0936\u0947\u0937 \u0915\u0940 \u0935\u094d\u092f\u093e\u0916\u094d\u092f\u093e<\/h2>\n<ul>\n<li style=\"text-align: justify;\">\n    <strong>\u00ab\u0936\u0947\u0937\u00bb \u0915\u093e \u0905\u0930\u094d\u0925 \u0915\u094d\u092f\u093e \u0939\u0948\u0964<\/strong> \u092f\u0926\u093f <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">b=qa+r<\/span><\/span>, \u0924\u094b <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">r=b-qa<\/span><\/span> \u0935\u0939 \u0939\u0948 \u091c\u094b <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">b<\/span><\/span> \u0938\u0947 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">qa<\/span><\/span> \u0917\u0941\u0923\u091c \u0918\u091f\u093e\u0928\u0947 \u092a\u0930 \u00ab\u092c\u091a\u0924\u093e\u00bb \u0939\u0948\u0964 \u0926\u0942\u0938\u0930\u0947 \u0936\u092c\u094d\u0926\u094b\u0902 \u092e\u0947\u0902, <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">r<\/span><\/span>, <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">a<\/span><\/span> \u0915\u0947 \u0917\u0941\u0923\u091c\u094b\u0902 \u0915\u0940 \u091c\u093e\u0932\u0940 \u092a\u0930 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">b<\/span><\/span> \u0915\u094b \u0938\u092e\u093e\u092f\u094b\u091c\u093f\u0924 \u0915\u0930\u0928\u0947 \u0915\u093e \u0905\u0935\u0936\u0947\u0937 \u0939\u0948\u0964\n  <\/li>\n<li style=\"text-align: justify;\">\n    <strong>\u0915\u094d\u092f\u094b\u0902 \u0906\u0935\u0936\u094d\u092f\u0915 \u0939\u0948<\/strong> <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">0\\le r&lt;|a|<\/span><\/span>\u0964 \u0907\u0938 \u0936\u0930\u094d\u0924 \u0915\u0947 \u092c\u093f\u0928\u093e, \u092f\u0941\u0917\u094d\u092e <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">(q,r)<\/span><\/span> \u090f\u0915\u093e\u0924\u094d\u092e\u0915 \u0928\u0939\u0940\u0902 \u0939\u094b\u0924\u093e\u0964 \u0935\u093e\u0938\u094d\u0924\u0935 \u092e\u0947\u0902, \u092f\u0926\u093f <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">b=qa+r<\/span><\/span>, \u0924\u094b <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">b=a(q+1)+(r-a)<\/span><\/span> \u092d\u0940 \u0938\u0924\u094d\u092f \u0939\u0948\u0964 \u0936\u0930\u094d\u0924 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">0\\le r&lt;|a|<\/span><\/span> \u0936\u0947\u0937 \u0915\u094b \u090f\u0915 \u0938\u094d\u0925\u093f\u0930 \u0916\u093f\u0921\u093c\u0915\u0940 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\{0,1,2,\\dots,|a|-1\\}<\/span><\/span> \u092e\u0947\u0902 \u0938\u0940\u092e\u093f\u0924 \u0915\u0930\u0924\u0940 \u0939\u0948, \u0914\u0930 \u0907\u0938 \u092a\u094d\u0930\u0915\u093e\u0930 \u0909\u0938\u0940 \u0938\u0902\u0916\u094d\u092f\u093e \u0915\u0940 \u0905\u0928\u0902\u0924 \u00ab\u092a\u0941\u0928\u0903-\u0932\u0947\u092c\u0932\u093f\u0902\u0917\u00bb \u0915\u094b \u0930\u094b\u0915\u0924\u0940 \u0939\u0948\u0964\n  <\/li>\n<li style=\"text-align: justify;\">\n    <strong>\u092f\u0926\u093f<\/strong> <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">a<\/span><\/span> <strong>\u090b\u0923\u093e\u0924\u094d\u092e\u0915 \u0939\u094b \u0924\u094b \u0915\u094d\u092f\u093e \u0939\u094b\u0924\u093e \u0939\u0948\u0964<\/strong> \u092a\u094d\u0930\u092e\u0947\u092f \u092c\u093f\u0928\u093e \u0915\u093f\u0938\u0940 \u092a\u0930\u093f\u0935\u0930\u094d\u0924\u0928 \u0915\u0947 \u092e\u093e\u0928\u094d\u092f \u0930\u0939\u0924\u093e \u0939\u0948: \u0936\u0947\u0937 \u0917\u0948\u0930-\u090b\u0923\u093e\u0924\u094d\u092e\u0915 \u0930\u0939\u0924\u093e \u0939\u0948 \u0914\u0930 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">|a|<\/span><\/span> \u0938\u0947 \u0938\u0940\u092e\u093f\u0924 \u0939\u094b\u0924\u093e \u0939\u0948\u0964 \u092f\u0939 \u0907\u0938\u0932\u093f\u090f \u092e\u0939\u0924\u094d\u0935\u092a\u0942\u0930\u094d\u0923 \u0939\u0948 \u0915\u094d\u092f\u094b\u0902\u0915\u093f \u0915\u0941\u091b \u092a\u094d\u0930\u094b\u0917\u094d\u0930\u093e\u092e\u093f\u0902\u0917 \u092d\u093e\u0937\u093e\u090f\u0901 \u0936\u0942\u0928\u094d\u092f \u0915\u0940 \u0913\u0930 \u091f\u094d\u0930\u0902\u0915\u0947\u0936\u0928 \u0915\u093e \u0909\u092a\u092f\u094b\u0917 \u0915\u0930\u0924\u0940 \u0939\u0948\u0902 \u0914\u0930 \u090b\u0923\u093e\u0924\u094d\u092e\u0915 \u0936\u0947\u0937 \u0909\u0924\u094d\u092a\u0928\u094d\u0928 \u0915\u0930 \u0938\u0915\u0924\u0940 \u0939\u0948\u0902, \u091c\u092c\u0915\u093f \u0917\u0923\u093f\u0924 \u092e\u0947\u0902 \u0936\u0947\u0937 \u0915\u094b \u00ab\u092e\u093e\u0928\u0915\u00bb \u092a\u094d\u0930\u0924\u093f\u0928\u093f\u0927\u093f \u092c\u0928\u093e\u0928\u0947 \u0915\u0947 \u0932\u093f\u090f \u092a\u0930\u0902\u092a\u0930\u093e <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">0\\le r&lt;|a|<\/span><\/span> \u0905\u092a\u0928\u093e\u0908 \u091c\u093e\u0924\u0940 \u0939\u0948\u0964<\/p>\n<p>    \u0907\u0938\u0915\u0947 \u0905\u0924\u093f\u0930\u093f\u0915\u094d\u0924, \u091c\u092c <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">a&gt;0<\/span><\/span> \u0939\u094b, \u0924\u094b \u092d\u093e\u0917\u092b\u0932 \u092b\u093c\u094d\u0932\u094b\u0930 \u0915\u0947 \u0938\u093e\u0925 \u092e\u0947\u0932 \u0916\u093e\u0924\u093e \u0939\u0948:<\/p>\n<p style=\"text-align:center;\" dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\nq=\\left\\lfloor \\frac{b}{a}\\right\\rfloor,\\qquad r=b-a\\left\\lfloor \\frac{b}{a}\\right\\rfloor.\n\n<\/span>\n<\/li>\n<\/ul>\n<p><a name=\"5\"><\/a><\/p>\n<h2>\u0932\u0902\u092c\u093e \u0935\u093f\u092d\u093e\u091c\u0928 \u090f\u0932\u094d\u0917\u094b\u0930\u093f\u0926\u094d\u092e<\/h2>\n<p><center><iframe class=\"lazyload\" width=\"560\" height=\"315\" data-src=\"https:\/\/www.youtube.com\/embed\/ABw4QYdD6Pg?si=eJiA7P6cD7RdlYYN\" title=\"YouTube video player\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture; web-share\" referrerpolicy=\"strict-origin-when-cross-origin\" allowfullscreen><\/iframe><\/center><\/p>\n<p>\u092f\u0942\u0915\u094d\u0932\u093f\u0921\u0940\u092f \u0935\u093f\u092d\u093e\u091c\u0928 \u0915\u0947 \u0906\u0927\u093e\u0930 \u092a\u0930 \u0938\u0902\u0916\u094d\u092f\u093e\u0913\u0902 \u0915\u0947 \u0938\u094d\u0925\u093e\u0928\u093f\u0915 \u0928\u093f\u0930\u0942\u092a\u0923 \u0915\u093e \u0909\u092a\u092f\u094b\u0917 \u0915\u0930\u0924\u0947 \u0939\u0941\u090f \u0932\u0902\u092c\u0947 \u0935\u093f\u092d\u093e\u091c\u0928 \u0915\u0947 \u090f\u0932\u094d\u0917\u094b\u0930\u093f\u0926\u094d\u092e \u0915\u094b \u0932\u093e\u0917\u0942 \u0915\u093f\u092f\u093e \u091c\u093e \u0938\u0915\u0924\u093e \u0939\u0948\u0964 \u092f\u0939 \u090f\u0932\u094d\u0917\u094b\u0930\u093f\u0926\u094d\u092e \u090f\u0915 \u0917\u0923\u0928\u093e\u0924\u094d\u092e\u0915 \u0924\u0915\u0928\u0940\u0915 \u0939\u0948 \u091c\u094b <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">a,b\\in\\mathbb{Z}<\/span><\/span> \u0914\u0930 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">a\\neq 0<\/span><\/span> \u0915\u0947 \u0938\u093e\u0925 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">b\\div a<\/span><\/span> \u0915\u0940 \u0917\u0923\u0928\u093e \u0915\u0930\u0924\u0947 \u0938\u092e\u092f <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">q<\/span><\/span> \u0914\u0930 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">r<\/span><\/span> \u0915\u0947 \u092e\u093e\u0928\u094b\u0902 \u0915\u094b \u0936\u0940\u0918\u094d\u0930\u0924\u093e \u0938\u0947 \u092a\u094d\u0930\u093e\u092a\u094d\u0924 \u0915\u0930\u0928\u0947 \u0915\u0940 \u0905\u0928\u0941\u092e\u0924\u093f \u0926\u0947\u0924\u093e \u0939\u0948\u0964<\/p>\n<p>\u0907\u0938\u0947 \u0935\u0930\u094d\u0923\u093f\u0924 \u0915\u0930\u0928\u0947 \u0915\u0947 \u0932\u093f\u090f, \u092a\u0939\u0932\u0947 \u0939\u092e \u0915\u0941\u091b \u0909\u0926\u093e\u0939\u0930\u0923\u094b\u0902 \u0915\u0940 \u0938\u092e\u0940\u0915\u094d\u0937\u093e \u0915\u0930\u0947\u0902\u0917\u0947 \u091c\u094b \u092a\u094d\u0930\u0915\u094d\u0930\u093f\u092f\u093e \u0914\u0930 \u090f\u0932\u094d\u0917\u094b\u0930\u093f\u0926\u094d\u092e \u0915\u0947 \u0928\u093f\u0937\u094d\u092a\u093e\u0926\u0928 \u0915\u0947 \u0926\u094c\u0930\u093e\u0928 \u0938\u0902\u092d\u093e\u0935\u093f\u0924 \u0938\u094d\u0925\u093f\u0924\u093f\u092f\u094b\u0902 \u0915\u094b \u0938\u094d\u092a\u0937\u094d\u091f \u0915\u0930\u0924\u0947 \u0939\u0948\u0902\u0964<\/p>\n<ol>\n<li>\n<p>\u092e\u093e\u0928 \u0932\u0947\u0902 \u0915\u093f \u0939\u092e <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">57\\div 4<\/span><\/span> \u0915\u0940 \u0917\u0923\u0928\u093e \u0915\u0930\u0928\u093e \u091a\u093e\u0939\u0924\u0947 \u0939\u0948\u0902\u0964 \u092f\u0939\u093e\u0901 57 <strong>\u092d\u093e\u091c\u094d\u092f<\/strong> \u0939\u0948 \u0914\u0930 4 <strong>\u092d\u093e\u091c\u0915<\/strong> \u0939\u0948\u0964 \u0907\u0938\u0947 \u0915\u0930\u0928\u0947 \u0915\u0947 \u0932\u093f\u090f \u0939\u092e \u0928\u093f\u092e\u094d\u0928\u0932\u093f\u0916\u093f\u0924 \u0917\u0923\u0928\u093e\u0913\u0902 \u0915\u093e \u0915\u094d\u0930\u092e \u0905\u092a\u0928\u093e\u090f\u0901\u0917\u0947:<\/p>\n<p style=\"text-align:center;\" dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\n\\begin{array}{rll}\n\n(1) &amp; \\color{red}57 \\div 4 =\\color{black}  \\\\ &amp; \\text{\u0935\u093f\u092d\u093e\u091c\u0928 \u0915\u0940 \u0915\u094d\u0930\u093f\u092f\u093e \u0932\u093f\u0916\u0947\u0902\u0964} \\\\ \\\\\n\n(2) &amp; \\color{red}5&#039;\\color{black}7 \\div 4 =  \\\\ &amp; \\text{\u092d\u093e\u091c\u094d\u092f \u0915\u093e \u092a\u0939\u0932\u093e \u0909\u092a\u0938\u0930\u094d\u0917 (\u092c\u093e\u090f\u0901 \u0938\u0947) \u0905\u0932\u0917 \u0915\u0930\u0947\u0902 \u091c\u094b}\\\\\n\n&amp;\\text{\u092d\u093e\u091c\u0915 \u0915\u0947 \u092c\u0930\u093e\u092c\u0930 \u092f\u093e \u0909\u0938\u0938\u0947 \u092c\u0921\u093c\u093e \u0939\u094b; \u0907\u0938 \u0938\u094d\u0925\u093f\u0924\u093f \u092e\u0947\u0902 5\u0964} \\\\ \\\\\n\n(3) &amp; 5&#039;7 \\div 4 = \\color{red}1\\color{black} \\\\ &amp; \\text{\u0909\u0938 \u0938\u092c\u0938\u0947 \u092c\u0921\u093c\u0947 \u0938\u0902\u0916\u094d\u092f\u093e \u0915\u0947 \u092c\u093e\u0930\u0947 \u092e\u0947\u0902 \u0938\u094b\u091a\u0947\u0902 \u091c\u094b $4$ \u0938\u0947 \u0917\u0941\u0923\u093e \u0915\u0930\u0928\u0947 \u092a\u0930}\\\\\n\n&amp;\\text{$5$ \u0938\u0947 \u0915\u092e \u092f\u093e \u092c\u0930\u093e\u092c\u0930 \u0939\u094b \u0914\u0930 \u0909\u0938\u0947 \u0938\u092e\u093e\u0928\u0924\u093e \u0915\u0947 \u0926\u093e\u090f\u0901 \u0932\u093f\u0916\u0947\u0902\u0964 \u092f\u0939 1 \u0939\u0948\u0964} \\\\ \\\\\n\n(4) &amp; \\begin{array}{ll}\\phantom{-|}5&#039;7 \\div 4 &amp;= 1 \\\\ \\color{red}-|\\underline{4}\\color{black} &amp; \\\\ \\color{red}\\phantom{-|}1\\color{black} &amp;  \\end{array} \\\\ &amp; \\text{\u092a\u0930\u093f\u0923\u093e\u092e \u0915\u094b \u092d\u093e\u091c\u0915 \u0938\u0947 \u0917\u0941\u0923\u093e \u0915\u0930\u0947\u0902 \u0914\u0930 \u091a\u092f\u0928\u093f\u0924 \u092e\u093e\u0928 \u0938\u0947 \u0918\u091f\u093e\u090f\u0901\u0964} \\\\ \\\\\n\n(5) &amp; \\begin{array}{ll}\\phantom{-|}5&#039;\\color{red}7&#039;\\color{black} \\div 4 &amp;= 1 \\\\ -|\\underline{4} &amp; \\\\ \\phantom{-|}1\\color{red}7\\color{black} &amp;  \\end{array} \\\\ &amp; \\text{\u0905\u0917\u0932\u0947 \u0905\u0902\u0915 \u0915\u093e \u091a\u092f\u0928 \u0915\u0930\u0947\u0902 \u0914\u0930 \u0909\u0938\u0947 \u00ab\u0928\u0940\u091a\u0947 \u0909\u0924\u093e\u0930\u0947\u0902\u00bb\u0964} \\\\ \\\\\n\n(6) &amp; \\begin{array}{ll}\\phantom{-|}5&#039;7&#039; \\div 4 &amp;= 1\\color{red}4\\color{black} \\\\ -|\\underline{4} &amp; \\\\ \\phantom{-|}17 &amp; \\\\ \\color{red}-|\\underline{16}\\color{black} &amp; \\\\ \\color{red}\\phantom{-|}1\\color{black}  \\end{array} \\\\ &amp; \\text{\u0905\u0902\u0924\u093f\u092e \u092a\u094d\u0930\u093e\u092a\u094d\u0924 \u0938\u0902\u0916\u094d\u092f\u093e \u0915\u0947 \u0938\u093e\u0925 \u0915\u094d\u0930\u092e \u0915\u094b \u0926\u094b\u0939\u0930\u093e\u090f\u0901\u0964}\n\n\\end{array}\n\n<\/span>\n<p>\u090f\u0932\u094d\u0917\u094b\u0930\u093f\u0926\u094d\u092e \u0924\u092c \u0938\u092e\u093e\u092a\u094d\u0924 \u0939\u094b\u0924\u093e \u0939\u0948 \u091c\u092c \u00ab\u0928\u0940\u091a\u0947 \u0909\u0924\u093e\u0930\u0928\u0947\u00bb \u0915\u0947 \u0932\u093f\u090f \u0905\u0902\u0915 \u0938\u092e\u093e\u092a\u094d\u0924 \u0939\u094b \u091c\u093e\u0924\u0947 \u0939\u0948\u0902, \u0914\u0930 \u092a\u0930\u093f\u0923\u093e\u092e\u0938\u094d\u0935\u0930\u0942\u092a \u092d\u093e\u0917\u092b\u0932 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">q=14<\/span><\/span> \u0924\u0925\u093e \u0936\u0947\u0937 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">r=1<\/span><\/span> \u092a\u094d\u0930\u093e\u092a\u094d\u0924 \u0939\u094b\u0924\u093e \u0939\u0948\u0964 \u0935\u093f\u0936\u0947\u0937 \u0930\u0942\u092a \u0938\u0947, \u0936\u0947\u0937 \u0939\u092e\u0947\u0936\u093e \u092d\u093e\u091c\u0915 \u0938\u0947 \u091b\u094b\u091f\u093e \u0939\u094b\u0917\u093e\u0964<\/p>\n<\/li>\n<li>\n<p>\u092e\u093e\u0928 \u0932\u0947\u0902 \u0915\u093f \u0939\u092e <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">132\\div 5<\/span><\/span> \u0915\u0940 \u0917\u0923\u0928\u093e \u0915\u0930\u0928\u093e \u091a\u093e\u0939\u0924\u0947 \u0939\u0948\u0902\u0964 \u0907\u0938\u0947 \u0915\u0930\u0928\u0947 \u0915\u0947 \u0932\u093f\u090f \u0939\u092e \u0928\u093f\u092e\u094d\u0928\u0932\u093f\u0916\u093f\u0924 \u0917\u0923\u0928\u093e\u0913\u0902 \u0915\u093e \u0915\u094d\u0930\u092e \u0905\u092a\u0928\u093e\u090f\u0901\u0917\u0947:<\/p>\n<p style=\"text-align:center;\" dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\begin{array}{rl}\n\n(1) &amp;1&#039;32 \\div 5 = \\\\\n\n&amp; \\text{\u092d\u093e\u091c\u094d\u092f \u0915\u093e \u092a\u0939\u0932\u093e \u0909\u092a\u0938\u0930\u094d\u0917 \u0905\u0932\u0917 \u0915\u0930\u0947\u0902 \u0914\u0930 \u0915\u093f\u0938\u0940 \u092a\u094d\u0930\u093e\u0915\u0943\u0924\u093f\u0915 \u0938\u0902\u0916\u094d\u092f\u093e \u0915\u094b \u0916\u094b\u091c\u0947\u0902 \u091c\u094b}\\\\\n\n&amp; \\text{5 \u0938\u0947 \u0917\u0941\u0923\u093e \u0915\u0930\u0928\u0947 \u092a\u0930 \u0909\u0938\u0938\u0947 \u0915\u092e \u092f\u093e \u092c\u0930\u093e\u092c\u0930 \u0939\u094b\u0964 \u092f\u0926\u093f \u0938\u0902\u092d\u0935 \u0928 \u0939\u094b,}\\\\\n\n&amp; \\text{\u0924\u094b \u0905\u0917\u0932\u0947 \u0905\u0902\u0915 \u0915\u094b \u0936\u093e\u092e\u093f\u0932 \u0915\u0930\u0947\u0902 \u091c\u092c \u0924\u0915 \u0915\u093f \u092f\u0939 \u0938\u0902\u092d\u0935 \u0928 \u0939\u094b \u091c\u093e\u090f\u0964} \\\\ \\\\\n\n(2) &amp;\\begin{array}{ll}\\phantom{-|}13&#039;2 \\div 5 &amp;= 2 \\\\ -|\\underline{10} &amp; \\\\ \\phantom{-|1}3 &amp; \\end{array}\\\\\n\n&amp; \\text{\u091c\u092c \u092a\u093f\u091b\u0932\u093e \u091a\u0930\u0923 \u0915\u093e\u0930\u094d\u092f \u0915\u0930\u0947, \u0924\u094b \u090f\u0932\u094d\u0917\u094b\u0930\u093f\u0926\u094d\u092e \u0915\u094b \u0938\u093e\u092e\u093e\u0928\u094d\u092f \u0930\u0942\u092a \u0938\u0947 \u0928\u093f\u0937\u094d\u092a\u093e\u0926\u093f\u0924 \u0915\u0930\u0947\u0902\u0964} \\\\ \\\\\n\n(3) &amp;\\begin{array}{ll}\\phantom{-|}13&#039;2&#039; \\div 5 &amp;= 26 \\\\ -|\\underline{10} &amp; \\\\ \\phantom{-|1}32 &amp;  \\\\ \\phantom{\\,} -|\\underline{30} &amp; \\\\ \\phantom{-|30} 2 &amp;  \\end{array}\n\n\\end{array}<\/span>\n<\/li>\n<li>\n<p>\u092f\u0926\u093f \u092d\u093e\u091c\u094d\u092f \u092e\u0947\u0902 \u0905\u0927\u093f\u0915 \u0905\u0902\u0915 \u0939\u094b\u0902, \u0924\u094b \u092a\u094d\u0930\u0915\u094d\u0930\u093f\u092f\u093e \u0909\u0938\u0940 \u092a\u094d\u0930\u0915\u093e\u0930 \u0928\u093f\u0937\u094d\u092a\u093e\u0926\u093f\u0924 \u0915\u0940 \u091c\u093e\u0924\u0940 \u0939\u0948\u0964 \u0909\u0926\u093e\u0939\u0930\u0923 \u0915\u0947 \u0932\u093f\u090f, <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">3521\\div 12<\/span><\/span> \u0915\u0940 \u0917\u0923\u0928\u093e \u0915\u0930\u0928\u0947 \u092a\u0930 \u092a\u094d\u0930\u093e\u092a\u094d\u0924 \u0939\u094b\u0924\u093e \u0939\u0948:<\/p>\n<p style=\"text-align:center;\" dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\begin{array}{ll}\n\n\\phantom{-|}35&#039;2&#039;1&#039; \\div 12 &amp; = 293 \\\\\n\n-|\\underline{24} &amp; \\\\\n\n\\phantom{-|}112 &amp; \\\\\n\n-|\\underline{108} &amp; \\\\\n\n\\phantom{-|10}41 &amp; \\\\\n\n\\phantom{0}-|\\underline{36} &amp; \\\\\n\n\\phantom{10-|}5 &amp; \\\\\n\n\\end{array}<\/span>\n<\/li>\n<li>\n<p>\u092f\u0926\u093f \u0938\u0902\u0916\u094d\u092f\u093e\u0913\u0902 \u092e\u0947\u0902 \u0938\u0947 \u0915\u094b\u0908 \u090f\u0915 \u090b\u0923\u093e\u0924\u094d\u092e\u0915 \u0939\u094b, \u0924\u094b \u092a\u0930\u093f\u0923\u093e\u092e \u092a\u094d\u0930\u0938\u094d\u0924\u0941\u0924 \u0915\u0930\u0928\u0947 \u0915\u0947 \u0926\u094b \u0938\u094d\u0935\u0940\u0915\u093e\u0930\u094d\u092f \u0924\u0930\u0940\u0915\u0947 \u0939\u094b\u0924\u0947 \u0939\u0948\u0902\u0964 \u0924\u0925\u093e\u092a\u093f, \u0938\u0902\u0916\u094d\u092f\u093e \u0938\u093f\u0926\u094d\u0927\u093e\u0902\u0924 \u092e\u0947\u0902 \u092e\u093e\u0928\u0915 \u0930\u0942\u092a \u0935\u0939 \u0939\u0948 \u091c\u093f\u0938\u092e\u0947\u0902 \u0936\u0947\u0937 \u0927\u0928\u093e\u0924\u094d\u092e\u0915 \u0939\u094b \u0914\u0930 \u0907\u0938 \u092a\u094d\u0930\u0915\u093e\u0930 \u092f\u0942\u0915\u094d\u0932\u093f\u0921\u0940\u092f \u0935\u093f\u092d\u093e\u091c\u0928 \u0915\u0947 \u0905\u0928\u0941\u0930\u0942\u092a \u0939\u094b\u0964 \u0909\u0926\u093e\u0939\u0930\u0923 \u0915\u0947 \u0932\u093f\u090f, \u092f\u0926\u093f \u0939\u092e <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">-598\\div 21<\/span><\/span> \u0915\u0940 \u0917\u0923\u0928\u093e \u0915\u0930\u0947\u0902, \u0924\u094b \u0928\u093f\u092e\u094d\u0928\u0932\u093f\u0916\u093f\u0924 \u0938\u0902\u092d\u093e\u0935\u093f\u0924 \u0935\u093f\u0915\u093e\u0938 \u092a\u094d\u0930\u093e\u092a\u094d\u0924 \u0939\u094b\u0924\u0947 \u0939\u0948\u0902, \u091c\u094b \u0926\u094b\u0928\u094b\u0902 \u0939\u0940 \u092a\u0939\u091a\u093e\u0928 \u0915\u0947 \u0930\u0942\u092a \u092e\u0947\u0902 \u0938\u0939\u0940 \u0939\u0948\u0902:<\/p>\n<ul>\n<li>\n        <b>\u090b\u0923\u093e\u0924\u094d\u092e\u0915 \u0936\u0947\u0937 \u0915\u0947 \u0938\u093e\u0925:<\/b> \u092f\u0939 \u0915\u094d\u0930\u093f\u092f\u093e \u0915\u0940 \u0936\u0941\u0930\u0941\u0906\u0924 \u092e\u0947\u0902 \u091a\u093f\u0939\u094d\u0928 \u0939\u091f\u093e\u0915\u0930 \u0914\u0930 \u0905\u0902\u0924 \u092e\u0947\u0902 \u0909\u0938\u0947 \u092a\u0941\u0928\u0903 \u0938\u094d\u0925\u093e\u092a\u093f\u0924 \u0915\u0930\u0915\u0947 \u092a\u094d\u0930\u093e\u092a\u094d\u0924 \u0915\u093f\u092f\u093e \u091c\u093e\u0924\u093e \u0939\u0948\u0964<\/p>\n<p style=\"text-align:center;\" dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\begin{array}{ll}\n\n\\phantom{-}59&#039;8&#039; \\div 21 &amp;= 28 \\\\\n\n-|\\underline{42} &amp; \\\\\n\n\\phantom{-|&#039;}178 &amp; \\\\\n\n\\phantom{\\,}-|\\underline{168} &amp; \\\\\n\n\\phantom{-|00}10 &amp; \\\\\n\n\\end{array}<\/span>\n<p>\u0907\u0938\u0938\u0947 \u092a\u094d\u0930\u093e\u092a\u094d\u0924 \u0939\u094b\u0924\u093e \u0939\u0948 \u0915\u093f:<\/p>\n<p style=\"text-align:center;\" dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">598 = 21 \\times 28 + 10<\/span>\n<p>\u092b\u093f\u0930, \u092f\u0926\u093f \u0939\u092e \u092a\u0942\u0930\u0940 \u0938\u092e\u093e\u0928\u0924\u093e \u0915\u094b <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">-1<\/span><\/span> \u0938\u0947 \u0917\u0941\u0923\u093e \u0915\u0930\u0947\u0902, \u0924\u094b \u092a\u094d\u0930\u093e\u092a\u094d\u0924 \u0939\u094b\u0924\u093e \u0939\u0948:<\/p>\n<p style=\"text-align:center;\" dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">-598 = 21 \\times (-28) - 10<\/span>\n<p>\u0905\u0924\u0903, \u0907\u0938 \u0928\u093f\u0930\u0942\u092a\u0923 \u092e\u0947\u0902 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">-598\\div 21<\/span><\/span> \u0915\u093e \u092a\u0930\u093f\u0923\u093e\u092e \u092d\u093e\u0917\u092b\u0932 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">q=-28<\/span><\/span> \u0914\u0930 \u0936\u0947\u0937 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">r=-10<\/span><\/span> \u0939\u094b\u0924\u093e \u0939\u0948\u0964<\/p>\n<p>\u0914\u0930 \u092f\u0926\u093f \u0939\u092e \u092a\u0942\u0930\u0940 \u0938\u092e\u093e\u0928\u0924\u093e \u0915\u094b \u092a\u0941\u0928\u0903 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">-1<\/span><\/span> \u0938\u0947 \u0917\u0941\u0923\u093e \u0915\u0930\u0947\u0902, \u0924\u094b \u092a\u094d\u0930\u093e\u092a\u094d\u0924 \u0939\u094b\u0924\u093e \u0939\u0948:<\/p>\n<p style=\"text-align:center;\" dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">598 = (-21)\\times(-28) + 10<\/span>\n<p>\u0905\u0924\u0903 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">598\\div (-21)<\/span><\/span> \u0915\u093e \u092a\u0930\u093f\u0923\u093e\u092e \u092d\u093e\u0917\u092b\u0932 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">q=-28<\/span><\/span> \u0914\u0930 \u0936\u0947\u0937 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">r=10<\/span><\/span> \u0939\u094b\u0924\u093e \u0939\u0948\u0964<\/p>\n<\/li>\n<li>\n        <b>\u0927\u0928\u093e\u0924\u094d\u092e\u0915 \u0936\u0947\u0937 \u0915\u0947 \u0938\u093e\u0925 \u0914\u0930 \u092f\u0942\u0915\u094d\u0932\u093f\u0921\u0940\u092f \u0935\u093f\u092d\u093e\u091c\u0928 \u0915\u0947 \u0905\u0928\u0941\u0930\u0942\u092a:<\/b> \u092a\u0942\u0930\u094d\u0935\u0935\u0930\u094d\u0924\u0940 \u0935\u093f\u0915\u093e\u0938 \u0938\u0947 \u092a\u094d\u0930\u093e\u092a\u094d\u0924 \u0939\u094b\u0924\u093e \u0939\u0948:<\/p>\n<p style=\"text-align:center;\" dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">-598 = 21 \\times (-28) - 10<\/span>\n<p>\u092b\u093f\u0930, \u0907\u0938 \u0938\u092e\u093e\u0928\u0924\u093e \u0915\u0947 \u0926\u093e\u090f\u0901 \u092a\u0915\u094d\u0937 \u092e\u0947\u0902 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">0=21-21<\/span><\/span> \u091c\u094b\u0921\u093c\u0928\u0947 \u092a\u0930 \u092a\u094d\u0930\u093e\u092a\u094d\u0924 \u0939\u094b\u0924\u093e \u0939\u0948:<\/p>\n<p style=\"text-align:center;\" dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">-598 = 21 \\times (-28) - 10 \\color{red}+ 21 - 21\\color{black} = 21\\times(-29) + 11<\/span>\n<p>\u0905\u0924\u0903, \u092f\u0942\u0915\u094d\u0932\u093f\u0921\u0940\u092f \u0935\u093f\u092d\u093e\u091c\u0928 \u0915\u0947 \u0905\u0928\u0941\u0930\u0942\u092a \u0930\u0939\u0924\u0947 \u0939\u0941\u090f, <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">-598\\div 21<\/span><\/span> \u0915\u0940 \u0917\u0923\u0928\u093e \u0915\u093e \u092a\u0930\u093f\u0923\u093e\u092e \u092d\u093e\u0917\u092b\u0932 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">q=-29<\/span><\/span> \u0914\u0930 \u0936\u0947\u0937 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">r=11<\/span><\/span> \u0926\u0947\u0924\u093e \u0939\u0948\u0964<\/p>\n<\/li>\n<\/ul>\n<p>\u092f\u0942\u0915\u094d\u0932\u093f\u0921\u0940\u092f \u0935\u093f\u092d\u093e\u091c\u0928 \u0915\u0940 \u092a\u0930\u0902\u092a\u0930\u093e \u0915\u0947 \u0905\u0928\u0941\u0938\u093e\u0930, \u0915\u0947\u0935\u0932 \u0927\u0928\u093e\u0924\u094d\u092e\u0915 \u0936\u0947\u0937 \u0935\u093e\u0932\u093e \u092a\u0930\u093f\u0923\u093e\u092e \u0939\u0940 \u092f\u0942\u0915\u094d\u0932\u093f\u0921\u0940\u092f \u092d\u093e\u0917\u092b\u0932 \u0914\u0930 \u0936\u0947\u0937 \u0915\u0947 \u0905\u0928\u0941\u0930\u0942\u092a \u0939\u094b\u0924\u093e \u0939\u0948\u0964 \u0924\u0925\u093e\u092a\u093f, \u0926\u094b\u0928\u094b\u0902 \u0905\u092d\u093f\u0935\u094d\u092f\u0915\u094d\u0924\u093f\u092f\u093e\u0901 \u0938\u0939\u0940 \u092a\u0939\u091a\u093e\u0928\u0947\u0902 \u0939\u0948\u0902 \u0914\u0930 \u0935\u093f\u092d\u093f\u0928\u094d\u0928 \u0938\u0902\u0926\u0930\u094d\u092d\u094b\u0902 \u092e\u0947\u0902 \u0909\u092a\u092f\u094b\u0917\u0940 \u0939\u094b \u0938\u0915\u0924\u0940 \u0939\u0948\u0902\u0964 \u092f\u0926\u094d\u092f\u092a\u093f \u0932\u0902\u092c\u093e \u0935\u093f\u092d\u093e\u091c\u0928 \u090f\u0932\u094d\u0917\u094b\u0930\u093f\u0926\u094d\u092e \u090b\u0923\u093e\u0924\u094d\u092e\u0915 \u0936\u0947\u0937 \u0909\u0924\u094d\u092a\u0928\u094d\u0928 \u0915\u0930 \u0938\u0915\u0924\u093e \u0939\u0948, \u092f\u0939 \u092f\u093e\u0902\u0924\u094d\u0930\u093f\u0915 \u0930\u0942\u092a \u0938\u0947 \u092a\u0930\u093f\u0923\u093e\u092e \u092a\u094d\u0930\u093e\u092a\u094d\u0924 \u0915\u0930\u0928\u0947 \u0914\u0930 \u0905\u0924\u093f\u0930\u093f\u0915\u094d\u0924 \u091a\u0930\u0923\u094b\u0902 \u0915\u0947 \u092c\u093f\u0928\u093e \u092c\u0940\u091c\u0940\u092f \u0939\u0947\u0930\u092b\u0947\u0930 \u0915\u0930\u0928\u0947 \u0915\u0947 \u0932\u093f\u090f \u0935\u094d\u092f\u093e\u0935\u0939\u093e\u0930\u093f\u0915 \u0939\u094b\u0924\u093e \u0939\u0948\u0964 \u0926\u0942\u0938\u0930\u0940 \u0913\u0930, \u0927\u0928\u093e\u0924\u094d\u092e\u0915 \u0936\u0947\u0937 \u0935\u093e\u0932\u0947 \u092a\u0930\u093f\u0923\u093e\u092e, \u091c\u094b \u092f\u0942\u0915\u094d\u0932\u093f\u0921\u0940\u092f \u0935\u093f\u092d\u093e\u091c\u0928 \u0915\u0947 \u0905\u0928\u0941\u0930\u0942\u092a \u0939\u094b\u0924\u0947 \u0939\u0948\u0902, \u092a\u094d\u0930\u0924\u094d\u092f\u0947\u0915 \u0905\u0935\u0936\u093f\u0937\u094d\u091f \u0935\u0930\u094d\u0917 \u0915\u0947 \u0932\u093f\u090f \u090f\u0915 \u0915\u0948\u0928\u094b\u0928\u093f\u0915\u0932 \u092a\u094d\u0930\u0924\u093f\u0928\u093f\u0927\u093f \u0928\u093f\u0930\u094d\u0927\u093e\u0930\u093f\u0924 \u0915\u0930\u0928\u0947 \u0915\u0940 \u0905\u0928\u0941\u092e\u0924\u093f \u0926\u0947\u0924\u0947 \u0939\u0948\u0902 (\u0909\u0926\u093e\u0939\u0930\u0923 \u0915\u0947 \u0932\u093f\u090f, <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\{0,1,\\dots,n-1\\}<\/span><\/span> \u092e\u0947\u0902), \u091c\u093f\u0938\u0938\u0947 \u092a\u0942\u0930\u094d\u0923\u093e\u0902\u0915\u094b\u0902 \u0915\u093e \u0938\u091f\u0940\u0915 \u0914\u0930 \u0905\u0938\u094d\u092a\u0937\u094d\u091f\u0924\u093e-\u0930\u0939\u093f\u0924 \u0935\u0930\u094d\u0917\u0940\u0915\u0930\u0923 \u0938\u0902\u092d\u0935 \u0939\u094b\u0924\u093e \u0939\u0948\u0964 \u092f\u0939 \u092d\u0940 \u0909\u0932\u094d\u0932\u0947\u0916\u0928\u0940\u092f \u0939\u0948 \u0915\u093f \u092a\u094d\u0930\u0924\u093f\u0928\u093f\u0927\u093f\u092f\u094b\u0902 \u0915\u0940 \u0905\u0928\u094d\u092f \u092a\u0930\u0902\u092a\u0930\u093e\u090f\u0901 \u092d\u0940 \u092e\u094c\u091c\u0942\u0926 \u0939\u0948\u0902, \u091c\u0948\u0938\u0947 \u0938\u092e\u092e\u093f\u0924 \u0905\u0935\u0936\u0947\u0937, \u091c\u094b \u090f\u0915 \u092c\u093e\u0930 \u0928\u093f\u092f\u092e \u0928\u093f\u0930\u094d\u0927\u093e\u0930\u093f\u0924 \u0939\u094b \u091c\u093e\u0928\u0947 \u092a\u0930 \u0938\u092e\u093e\u0928 \u0930\u0942\u092a \u0938\u0947 \u092e\u093e\u0928\u094d\u092f \u0939\u094b\u0924\u0940 \u0939\u0948\u0902\u0964<\/p>\n<\/li>\n<\/ol>\n<p><a name=\"6\"><\/a><\/p>\n<h2>\u0928\u093f\u0937\u094d\u0915\u0930\u094d\u0937<\/h2>\n<p>\u0935\u093f\u092d\u093e\u091c\u0928 \u0915\u093e \u090f\u0932\u094d\u0917\u094b\u0930\u093f\u0926\u094d\u092e \u092f\u0939 \u0938\u0941\u0928\u093f\u0936\u094d\u091a\u093f\u0924 \u0915\u0930\u0924\u093e \u0939\u0948 \u0915\u093f \u092a\u094d\u0930\u0924\u094d\u092f\u0947\u0915 \u092a\u0942\u0930\u094d\u0923\u093e\u0902\u0915 \u0935\u093f\u092d\u093e\u091c\u0928 \u0915\u094b \u0905\u0926\u094d\u0935\u093f\u0924\u0940\u092f \u0930\u0942\u092a \u0938\u0947 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">b=qa+r<\/span><\/span> \u0915\u0947 \u0930\u0942\u092a \u092e\u0947\u0902 \u0935\u094d\u092f\u0915\u094d\u0924 \u0915\u093f\u092f\u093e \u091c\u093e \u0938\u0915\u0924\u093e \u0939\u0948, \u091c\u0939\u093e\u0901 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">0\\le r&lt;|a|<\/span><\/span> \u0939\u094b\u0924\u093e \u0939\u0948\u0964 \u0907\u0938\u0938\u0947 \u092d\u093e\u0917\u092b\u0932 \u0914\u0930 \u0936\u0947\u0937 \u0915\u0940 \u0935\u094d\u092f\u093e\u0916\u094d\u092f\u093e \u0915\u0947 \u0932\u093f\u090f \u090f\u0915 \u092e\u093e\u0928\u0915 \u092e\u093e\u0928\u0926\u0902\u0921 \u0938\u094d\u0925\u093e\u092a\u093f\u0924 \u0939\u094b\u0924\u093e \u0939\u0948, \u092f\u0939\u093e\u0901 \u0924\u0915 \u0915\u093f \u091c\u092c \u090b\u0923\u093e\u0924\u094d\u092e\u0915 \u0938\u0902\u0916\u094d\u092f\u093e\u090f\u0901 \u0938\u092e\u094d\u092e\u093f\u0932\u093f\u0924 \u0939\u094b\u0902\u0964 \u0932\u0902\u092c\u093e \u0935\u093f\u092d\u093e\u091c\u0928 \u090f\u0932\u094d\u0917\u094b\u0930\u093f\u0926\u094d\u092e \u0907\u0938 \u0935\u093f\u0918\u091f\u0928 \u0915\u093e \u0915\u0947\u0935\u0932 \u090f\u0915 \u0935\u094d\u092f\u093e\u0935\u0939\u093e\u0930\u093f\u0915 \u0915\u093e\u0930\u094d\u092f\u093e\u0928\u094d\u0935\u092f\u0928 \u0939\u0948, \u091c\u094b \u0938\u094d\u0925\u093e\u0928\u093f\u0915 \u0928\u093f\u0930\u0942\u092a\u0923 \u092a\u0930 \u0906\u0927\u093e\u0930\u093f\u0924 \u0939\u0948 \u0914\u0930 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">q<\/span><\/span> \u0924\u0925\u093e <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">r<\/span><\/span> \u0915\u0940 \u0917\u0923\u0928\u093e \u092f\u093e\u0902\u0924\u094d\u0930\u093f\u0915 \u0930\u0942\u092a \u0938\u0947 \u0915\u0930\u0928\u0947 \u0915\u0940 \u0905\u0928\u0941\u092e\u0924\u093f \u0926\u0947\u0924\u093e \u0939\u0948\u0964 \u0905\u0902\u0924\u0924\u0903, \u092f\u0939 \u092f\u0942\u0915\u094d\u0932\u093f\u0921\u0940\u092f \u0930\u0942\u092a \u0928 \u0915\u0947\u0935\u0932 \u0905\u0938\u094d\u092a\u0937\u094d\u091f\u0924\u093e\u0913\u0902 \u0938\u0947 \u092c\u091a\u093e\u0924\u093e \u0939\u0948, \u092c\u0932\u094d\u0915\u093f \u092e\u0949\u0921\u094d\u092f\u0942\u0932\u0930 \u0905\u0902\u0915\u0917\u0923\u093f\u0924 \u0915\u0947 \u0938\u093e\u0925 \u092d\u0940 \u0938\u094d\u0935\u093e\u092d\u093e\u0935\u093f\u0915 \u0930\u0942\u092a \u0938\u0947 \u091c\u0941\u0921\u093c\u0924\u093e \u0939\u0948: \u0936\u0947\u0937 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">r<\/span><\/span>, <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">a<\/span><\/span> \u092e\u093e\u092a\u093e\u0902\u0915 \u0915\u0947 \u0905\u0928\u0941\u0938\u093e\u0930 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">b<\/span><\/span> \u0915\u0940 \u0905\u0935\u0936\u093f\u0937\u094d\u091f \u0936\u094d\u0930\u0947\u0923\u0940 \u0915\u093e \u090f\u0915 \u0915\u0948\u0928\u094b\u0928\u093f\u0915\u0932 \u092a\u094d\u0930\u0924\u093f\u0928\u093f\u0927\u093f \u0915\u0947 \u0930\u0942\u092a \u092e\u0947\u0902 \u0915\u093e\u0930\u094d\u092f \u0915\u0930\u0924\u093e \u0939\u0948, \u091c\u094b \u0938\u0902\u0916\u094d\u092f\u093e \u0938\u093f\u0926\u094d\u0927\u093e\u0902\u0924 \u0924\u0925\u093e \u0938\u0902\u0917\u0923\u0915\u0940\u092f \u0905\u0928\u0941\u092a\u094d\u0930\u092f\u094b\u0917\u094b\u0902 \u0915\u0940 \u0905\u0928\u0947\u0915 \u0924\u0915\u0928\u0940\u0915\u094b\u0902 \u0915\u093e \u0906\u0927\u093e\u0930 \u0939\u0948, \u091c\u093f\u0928\u094d\u0939\u0947\u0902 \u0906\u0917\u093e\u092e\u0940 \u092a\u094d\u0930\u0938\u094d\u0924\u0941\u0924\u093f\u092f\u094b\u0902 \u092e\u0947\u0902 \u0926\u0947\u0916\u093e \u091c\u093e\u090f\u0917\u093e\u0964<\/p>\n<p><a name=\"7\"><\/a><\/p>\n<h2>\u092a\u094d\u0930\u0938\u094d\u0924\u093e\u0935\u093f\u0924 \u0914\u0930 \u0939\u0932 \u0915\u093f\u090f \u0917\u090f \u0905\u092d\u094d\u092f\u093e\u0938<\/h2>\n<h3>\u092f\u0942\u0915\u094d\u0932\u093f\u0921\u0940\u092f \u0935\u093f\u092d\u093e\u091c\u0928<\/h3>\n<ol>\n<li><strong>(\u0939\u0932 \u0915\u093f\u092f\u093e \u0917\u092f\u093e)<\/strong> \u0910\u0938\u0947 <span class=\"katex-eq\" data-katex-display=\"false\">q<\/span> \u0914\u0930 <span class=\"katex-eq\" data-katex-display=\"false\">r<\/span> \u091c\u094d\u091e\u093e\u0924 \u0915\u0930\u0947\u0902 \u0915\u093f\n<p style=\"text-align:center;\" dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">137 = 9q + r,\\qquad 0\\le r\\lt 9.<\/span>\n<p><strong>\u0938\u092e\u093e\u0927\u093e\u0928:<\/strong> \u0909\u0938 \u0938\u092c\u0938\u0947 \u092c\u0921\u093c\u0947 \u0938\u0902\u0916\u094d\u092f\u093e \u0915\u094b \u0916\u094b\u091c\u0947\u0902 \u091c\u094b <span class=\"katex-eq\" data-katex-display=\"false\">9<\/span> \u0938\u0947 \u0917\u0941\u0923\u093e \u0915\u0930\u0928\u0947 \u092a\u0930 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">137<\/span><\/span> \u0938\u0947 \u0905\u0927\u093f\u0915 \u0928 \u0939\u094b\u0964 \u0939\u092e\u093e\u0930\u0947 \u092a\u093e\u0938 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">15\\times 9 = 135<\/span><\/span> \u0914\u0930 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">16\\times 9 = 144<\/span><\/span> \u0939\u0948\u0902, \u0905\u0924\u0903 \u0935\u093e\u0902\u091b\u093f\u0924 \u092d\u093e\u0917\u092b\u0932 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">q=15<\/span><\/span> \u0939\u0948\u0964 \u0905\u092c \u0936\u0947\u0937 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">r=137-9q<\/span><\/span> \u0915\u0940 \u0917\u0923\u0928\u093e \u0915\u0930\u0947\u0902 \u0914\u0930 \u091c\u093e\u0901\u091a\u0947\u0902 \u0915\u093f <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">0\\le r\\lt 9<\/span><\/span>\u0964 \u0938\u0924\u094d\u092f\u093e\u092a\u0928 \u0915\u0930\u0928\u0947 \u092a\u0930 \u092a\u094d\u0930\u093e\u092a\u094d\u0924 \u0939\u094b\u0924\u093e \u0939\u0948:<\/p>\n<p style=\"text-align:center;\" dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\nr=137-9\\cdot 15=137-135=2.\n\n<\/span>\n<p>\u0905\u0924\u0903 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">137=9\\cdot 15+2<\/span><\/span> \u0939\u0948, \u091c\u0939\u093e\u0901 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">0\\le 2\\lt 9<\/span><\/span>\u0964<\/p>\n<\/li>\n<li><strong>(\u0939\u0932 \u0915\u093f\u092f\u093e \u0917\u092f\u093e)<\/strong> \u0910\u0938\u0947 <span class=\"katex-eq\" data-katex-display=\"false\">q<\/span> \u0914\u0930 <span class=\"katex-eq\" data-katex-display=\"false\">r<\/span> \u091c\u094d\u091e\u093e\u0924 \u0915\u0930\u0947\u0902 \u0915\u093f\n<p style=\"text-align:center;\" dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">2025 = 37q + r,\\qquad 0\\le r\\lt 37.<\/span>\n<p><strong>\u0938\u092e\u093e\u0927\u093e\u0928:<\/strong> \u0909\u0938 \u0938\u092c\u0938\u0947 \u092c\u0921\u093c\u0947 \u0938\u0902\u0916\u094d\u092f\u093e \u0915\u094b \u0916\u094b\u091c\u0947\u0902 \u091c\u094b <span class=\"katex-eq\" data-katex-display=\"false\">37<\/span> \u0938\u0947 \u0917\u0941\u0923\u093e \u0915\u0930\u0928\u0947 \u092a\u0930 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">2025<\/span><\/span> \u0938\u0947 \u0905\u0927\u093f\u0915 \u0928 \u0939\u094b\u0964 \u0927\u094d\u092f\u093e\u0928 \u0926\u0947\u0902 \u0915\u093f <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">37\\times 54 = 1998<\/span><\/span> \u0914\u0930 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">37\\times 55 = 2035<\/span><\/span> \u0939\u0948\u0902, \u0905\u0924\u0903 \u0935\u093e\u0902\u091b\u093f\u0924 \u092d\u093e\u0917\u092b\u0932 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">q=54<\/span><\/span> \u0939\u0948\u0964 \u0905\u092c \u0936\u0947\u0937 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">r=2025-37q<\/span><\/span> \u0915\u0940 \u0917\u0923\u0928\u093e \u0915\u0930\u0947\u0902 \u0914\u0930 \u091c\u093e\u0901\u091a\u0947\u0902 \u0915\u093f <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">0\\le r\\lt 37<\/span><\/span>\u0964 \u0938\u0924\u094d\u092f\u093e\u092a\u0928 \u0915\u0930\u0928\u0947 \u092a\u0930 \u092a\u094d\u0930\u093e\u092a\u094d\u0924 \u0939\u094b\u0924\u093e \u0939\u0948:<\/p>\n<p style=\"text-align:center;\" dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\nr=2025-37\\cdot 54=2025-1998=27.\n\n<\/span>\n<p>\u0905\u0924\u0903 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">2025=37\\cdot 54+27<\/span><\/span> \u0939\u0948, \u091c\u0939\u093e\u0901 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">0\\le 27\\lt 37<\/span><\/span>\u0964<\/p>\n<\/li>\n<li>\u0910\u0938\u0947 <span class=\"katex-eq\" data-katex-display=\"false\">q<\/span> \u0914\u0930 <span class=\"katex-eq\" data-katex-display=\"false\">r<\/span> \u091c\u094d\u091e\u093e\u0924 \u0915\u0930\u0947\u0902 \u0915\u093f\n<p style=\"text-align:center;\" dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">745 = 23q + r,\\qquad 0\\le r\\lt 23.<\/span>\n<\/li>\n<li>\u0910\u0938\u0947 <span class=\"katex-eq\" data-katex-display=\"false\">q<\/span> \u0914\u0930 <span class=\"katex-eq\" data-katex-display=\"false\">r<\/span> \u091c\u094d\u091e\u093e\u0924 \u0915\u0930\u0947\u0902 \u0915\u093f\n<p style=\"text-align:center;\" dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">-314 = 11q + r,\\qquad 0\\le r\\lt 11.<\/span>\n<\/li>\n<li>\u0910\u0938\u0947 <span class=\"katex-eq\" data-katex-display=\"false\">q<\/span> \u0914\u0930 <span class=\"katex-eq\" data-katex-display=\"false\">r<\/span> \u091c\u094d\u091e\u093e\u0924 \u0915\u0930\u0947\u0902 \u0915\u093f\n<p style=\"text-align:center;\" dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">598 = (-21)q + r,\\qquad 0\\le r\\lt |-21|.<\/span>\n<\/li>\n<li><strong>\u0928\u093f\u092f\u0924 \u0936\u0947\u0937 \u0914\u0930 \u092a\u0942\u0930\u094d\u0923\u093e\u0902\u0915\u094b\u0902 \u0915\u0940 \u0916\u094b\u091c\u0964<\/strong> \u092e\u093e\u0928 \u0932\u0947\u0902 \u0915\u093f <span class=\"katex-eq\" data-katex-display=\"false\">a=12<\/span> \u0939\u0948\u0964\n<p>(a) \u0909\u0928 \u0938\u092d\u0940 \u092a\u0942\u0930\u094d\u0923\u093e\u0902\u0915\u094b\u0902 <span class=\"katex-eq\" data-katex-display=\"false\">b<\/span> \u0915\u0947 \u0938\u092e\u0941\u091a\u094d\u091a\u092f \u0915\u093e \u0935\u0930\u094d\u0923\u0928 \u0915\u0930\u0947\u0902 \u091c\u093f\u0928\u0915\u0940 <span class=\"katex-eq\" data-katex-display=\"false\">12<\/span> \u0938\u0947 \u092f\u0942\u0915\u094d\u0932\u093f\u0921\u0940\u092f \u0935\u093f\u092d\u093e\u091c\u0928 \u092e\u0947\u0902 \u0936\u0947\u0937 <span class=\"katex-eq\" data-katex-display=\"false\">r=5<\/span> \u0939\u0948\u0964<\/p>\n<p>(b) \u0910\u0938\u093e \u0928\u094d\u092f\u0942\u0928\u0924\u092e \u092a\u0942\u0930\u094d\u0923\u093e\u0902\u0915 <span class=\"katex-eq\" data-katex-display=\"false\">b\\gt 1000<\/span> \u091c\u094d\u091e\u093e\u0924 \u0915\u0930\u0947\u0902 \u091c\u094b \u0909\u092a\u0930\u094d\u092f\u0941\u0915\u094d\u0924 \u0936\u0930\u094d\u0924 \u0915\u094b \u092a\u0942\u0930\u093e \u0915\u0930\u0924\u093e \u0939\u094b \u0914\u0930 \u0938\u0902\u092c\u0902\u0927\u093f\u0924 \u092d\u093e\u0917\u092b\u0932 <span class=\"katex-eq\" data-katex-display=\"false\">q<\/span> \u0928\u093f\u0930\u094d\u0927\u093e\u0930\u093f\u0924 \u0915\u0930\u0947\u0902\u0964<\/p>\n<\/li>\n<\/ol>\n<h3>\u0932\u0902\u092c\u093e \u0935\u093f\u092d\u093e\u091c\u0928 \u090f\u0932\u094d\u0917\u094b\u0930\u093f\u0926\u094d\u092e<\/h3>\n<p>\u092a\u094d\u0930\u0924\u094d\u092f\u0947\u0915 \u092e\u093e\u092e\u0932\u0947 \u092e\u0947\u0902, \u092d\u093e\u0917\u092b\u0932 <span class=\"katex-eq\" data-katex-display=\"false\">q<\/span> \u0914\u0930 \u0936\u0947\u0937 <span class=\"katex-eq\" data-katex-display=\"false\">r<\/span> \u0915\u0940 \u0917\u0923\u0928\u093e \u0915\u0930\u0928\u0947 \u0915\u0947 \u0932\u093f\u090f \u0932\u0902\u092c\u0947 \u0935\u093f\u092d\u093e\u091c\u0928 \u0915\u0947 \u090f\u0932\u094d\u0917\u094b\u0930\u093f\u0926\u094d\u092e \u0915\u094b \u0932\u093e\u0917\u0942 \u0915\u0930\u0947\u0902\u0964 \u091c\u092c \u090f\u0932\u094d\u0917\u094b\u0930\u093f\u0926\u094d\u092e \u090b\u0923\u093e\u0924\u094d\u092e\u0915 \u0936\u0947\u0937 \u092a\u094d\u0930\u0926\u093e\u0928 \u0915\u0930\u0947, \u0924\u092c \u092a\u0930\u093f\u0923\u093e\u092e \u0915\u094b \u092f\u0942\u0915\u094d\u0932\u093f\u0921\u0940\u092f \u0935\u093f\u092d\u093e\u091c\u0928 \u0915\u0947 \u0930\u0942\u092a \u092e\u0947\u0902 \u092a\u0930\u093f\u0935\u0930\u094d\u0924\u093f\u0924 \u0915\u0930\u0947\u0902\u0964\n<\/p>\n<ol>\n<li><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">84\\div 6.<\/span><\/span><\/li>\n<li><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">197\\div 8.<\/span><\/span><\/li>\n<li><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">1256\\div 7.<\/span><\/span><\/li>\n<li><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">-3521\\div 12.<\/span><\/span><\/li>\n<li><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">-98765\\div 24.<\/span><\/span><\/li>\n<li><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">845\\div -13.<\/span><\/span><\/li>\n<li><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">-12345\\div 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\u092d\u093e\u0917\u092b\u0932 \u0914\u0930 \u0936\u0947\u0937 \u0915\u0940 \u0905\u0938\u094d\u0924\u093f\u0924\u094d\u0935 \u0915\u094b \u0938\u093f\u0926\u094d\u0927 \u0915\u093f\u092f\u093e \u091c\u093e\u0924\u093e \u0939\u0948 \u0914\u0930 \u0909\u0938\u0915\u0947 \u092c\u093e\u0926 \u0909\u0928\u0915\u0940 \u090f\u0915\u093e\u0924\u094d\u092e\u0915\u0924\u093e \u0915\u094b\u0964 \u0905\u0902\u0924\u0924\u0903, \u0936\u0947\u0937 \u0915\u0947 \u0905\u0930\u094d\u0925 \u0915\u0940 \u0935\u094d\u092f\u093e\u0916\u094d\u092f\u093e [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":35980,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"iawp_total_views":0,"footnotes":""},"categories":[577,1410],"tags":[],"class_list":["post-35998","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-577","category-1410"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin 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