{"id":36018,"date":"2026-01-10T18:40:41","date_gmt":"2026-01-10T18:40:41","guid":{"rendered":"https:\/\/toposuranos.com\/material\/?p=36018"},"modified":"2026-01-10T18:40:41","modified_gmt":"2026-01-10T18:40:41","slug":"%e3%83%a6%e3%83%bc%e3%82%af%e3%83%aa%e3%83%83%e3%83%89%e9%99%a4%e6%b3%95%e3%81%ae%e3%82%a2%e3%83%ab%e3%82%b4%e3%83%aa%e3%82%ba%e3%83%a0","status":"publish","type":"post","link":"https:\/\/toposuranos.com\/material\/ja\/%e3%83%a6%e3%83%bc%e3%82%af%e3%83%aa%e3%83%83%e3%83%89%e9%99%a4%e6%b3%95%e3%81%ae%e3%82%a2%e3%83%ab%e3%82%b4%e3%83%aa%e3%82%ba%e3%83%a0\/","title":{"rendered":"\u30e6\u30fc\u30af\u30ea\u30c3\u30c9\u9664\u6cd5\u306e\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0"},"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>\u9664\u6cd5\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0<\/h1>\n<p style=\"text-align:center;\"><em>\u672c\u8b1b\u3067\u306f\u3001\u6574\u6570\u306b\u5bfe\u3057\u3066\u4e00\u610f\u306a\u5206\u89e3 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">b=qa+r<\/span><\/span>\uff08<span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">0\\le r&lt;|a|<\/span><\/span> \u3092\u6e80\u305f\u3059\uff09\u3092\u5f62\u5f0f\u5316\u3059\u308b\u539f\u7406\u3068\u3057\u3066\u3001<strong>\u9664\u6cd5\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0<\/strong>\u3092\u5c55\u958b\u3059\u308b\u3002\u307e\u305a\u5546\u3068\u4f59\u308a\u306e<strong>\u5b58\u5728<\/strong>\u3092\u8a3c\u660e\u3057\u3001\u6b21\u306b\u305d\u306e<strong>\u4e00\u610f\u6027<\/strong>\u3092\u793a\u3059\u3002\u6700\u5f8c\u306b\u3001\u4f59\u308a\u306e\u610f\u5473\u3092\u89e3\u91c8\u3057\u3001\u7406\u8ad6\u3092\u8a08\u7b97\u624b\u7d9a\u304d\u3068\u3057\u3066\u306e<strong>\u7b46\u7b97\u306b\u3088\u308b\u9664\u6cd5\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0<\/strong>\u3068\u7d50\u3073\u4ed8\u3051\u3001\u3055\u3089\u306b\u5408\u540c\u7b97\u8853\u304a\u3088\u3073\u8a08\u7b97\u6a5f\u5fdc\u7528\u3068\u306e\u81ea\u7136\u306a\u95a2\u9023\u3092\u4e88\u544a\u3059\u308b\u3002<\/em><\/p>\n<p style=\"text-align:center;\"><strong>\u5b66\u7fd2\u76ee\u6a19<\/strong><\/p>\n<p>\u672c\u8b1b\u3092\u4fee\u4e86\u3059\u308b\u3068\u3001\u5b66\u751f\u306f\u6b21\u306e\u3053\u3068\u304c\u3067\u304d\u308b\u3088\u3046\u306b\u306a\u308b\u3002<\/p>\n<ol>\n<li><strong>\u8b58\u5225\u3059\u308b<\/strong>\uff1a\u6574\u6570\u9664\u6cd5\u306b\u304a\u3051\u308b\u57fa\u672c\u7684\u6982\u5ff5\u304a\u3088\u3073\u5f79\u5272\uff08\u88ab\u9664\u6570\u3001\u9664\u6570\u3001\u5546\u3001\u4f59\u308a\uff09\u3068\u3001\u53b3\u5bc6\u306a\u5834\u5408\u3068\u3057\u3066\u306e\u53ef\u9664\u6027\u306e\u6982\u5ff5\u3002<\/li>\n<li><strong>\u8aac\u660e\u3059\u308b<\/strong>\uff1a\u30e6\u30fc\u30af\u30ea\u30c3\u30c9\u9664\u6cd5\u306e\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\uff0f\u5b9a\u7406\u306e\u547d\u984c\u3001\u4f59\u308a\u3092\u898f\u5b9a\u3059\u308b\u6761\u4ef6\uff08<span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">0\\le r&lt;|a|<\/span><\/span>\uff09\u304a\u3088\u3073\u66d6\u6627\u3055\u3092\u907f\u3051\u308b\u305f\u3081\u306e\u305d\u306e\u76ee\u7684\u3002<\/li>\n<li><strong>\u9069\u7528\u3059\u308b<\/strong>\uff1a\u5177\u4f53\u4f8b\u306b\u304a\u3044\u3066\u3001\u30e6\u30fc\u30af\u30ea\u30c3\u30c9\u5206\u89e3 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">b=qa+r<\/span><\/span> \u3092\u7528\u3044\u3066 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">q<\/span><\/span> \u3068 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">r<\/span><\/span> \u3092\u6c7a\u5b9a\u3057\u3001\u4f59\u308a\u306e\u4e0a\u754c\u3092\u78ba\u8a8d\u3059\u308b\u3002<\/li>\n<li><strong>\u5206\u6790\u3059\u308b<\/strong>\uff1a\u88ab\u9664\u6570\u304a\u3088\u3073\u9664\u6570\u306e\u7b26\u53f7\u306b\u5fdc\u3058\u305f\u5834\u5408\u5206\u3051\u306e\u6271\u3044\u3092\u691c\u8a0e\u3057\u3001\u30e6\u30fc\u30af\u30ea\u30c3\u30c9\u306e\u898f\u7d04\u304c\u4f59\u308a\u3092\u975e\u8ca0\u306b\u4fdd\u3064\u7406\u7531\u3092\u6b63\u5f53\u5316\u3059\u308b\u3002<\/li>\n<li><strong>\u5b9f\u884c\u3059\u308b<\/strong>\uff1a\u4f4d\u53d6\u308a\u8868\u73fe\u306b\u57fa\u3065\u304f\u6a5f\u68b0\u7684\u624b\u7d9a\u304d\u3068\u3057\u3066\u306e\u7b46\u7b97\u306b\u3088\u308b\u9664\u6cd5\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u3092\u5b9f\u884c\u3057\u3001 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">q<\/span><\/span> \u3068 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">r<\/span><\/span> \u3092\u5f97\u308b\u3002<\/li>\n<\/ol>\n<p style=\"text-align:center;\"><b><u>\u5185\u5bb9\u7d22\u5f15<\/u>:<\/b><br \/>\n<a href=\"#1\">\u9664\u6cd5\u3068\u53ef\u9664\u6027<\/a><br \/>\n<a href=\"#2\">\u30e6\u30fc\u30af\u30ea\u30c3\u30c9\u9664\u6cd5\u306e\u5b9a\u7406<\/a><br \/>\n<a href=\"#3\">\u30e6\u30fc\u30af\u30ea\u30c3\u30c9\u9664\u6cd5\u306e\u8a3c\u660e<\/a><br \/>\n<a href=\"#4\">\u5546\u3068\u4f59\u308a\u306e\u89e3\u91c8<\/a><br \/>\n<a href=\"#5\">\u7b46\u7b97\u306b\u3088\u308b\u9664\u6cd5\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0<\/a><br \/>\n<a href=\"#6\">\u7d50\u8ad6<\/a><br \/>\n<a href=\"#7\">\u6f14\u7fd2\u554f\u984c\uff08\u4f8b\u984c\u30fb\u89e3\u7b54\u4ed8\u304d\uff09<\/a>\n<\/p>\n<p><a name=\"1\"><\/a><\/p>\n<h2>\u9664\u6cd5\u3068\u53ef\u9664\u6027<\/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>\u7b97\u8853\u306b\u304a\u3044\u3066\u3001\u53ef\u9664\u6027\u306f\u300c\u53b3\u5bc6\u306a\u300d\u5834\u5408\u3092\u8868\u3059\u3002\u3059\u306a\u308f\u3061\u3001<span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">a\\mid b<\/span><\/span> \u306f\u3001<span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">b<\/span><\/span> \u304c <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">a<\/span><\/span> \u306e\u500d\u6570\u3068\u3057\u3066\u6b63\u78ba\u306b\u8868\u3055\u308c\u308b\u3053\u3068\u3092\u610f\u5473\u3059\u308b\u3002\u3057\u304b\u3057\u3001\u4efb\u610f\u306e\u4e8c\u3064\u306e\u6574\u6570\u306e\u9593\u306b\u5e38\u306b\u53ef\u9664\u6027\u304c\u6210\u308a\u7acb\u3064\u308f\u3051\u3067\u306f\u306a\u3044\u3002\u305d\u308c\u3067\u3082\u306a\u304a\u3001\u300c\u3042\u308b\u6570\u304c\u5225\u306e\u6570\u306b\u4f55\u56de\u542b\u307e\u308c\u308b\u304b\u3001\u305d\u3057\u3066\u6b63\u78ba\u306b\u542b\u307e\u308c\u306a\u3044\u5834\u5408\u306b\u4f55\u304c\u6b8b\u308b\u306e\u304b\u300d\u3092\u554f\u3046\u3053\u3068\u306f\u3067\u304d\u308b\u3002\u3053\u306e\u6587\u8108\u306b\u304a\u3044\u3066<strong>\u9664\u6cd5\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0<\/strong>\u304c\u73fe\u308c\u3001\u4efb\u610f\u306e\u6574\u6570 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">b<\/span><\/span> \u304c <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">a<\/span><\/span> \u306e\u500d\u6570\u3068\u300c\u4f59\u308a\u300d\u306e\u548c\u3068\u3057\u3066\u8868\u3055\u308c\u308b\u3053\u3068\u3092\u4fdd\u8a3c\u3059\u308b\u3002<\/p>\n<p>\u4f8b\u3068\u3057\u3066\u3001<span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">a=3<\/span><\/span> \u304a\u3088\u3073 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">b=16<\/span><\/span> \u3092\u8003\u3048\u308b\u30023 \u306f 16 \u3092\u5272\u308a\u5207\u3089\u306a\u3044\u3053\u3068\u306f\u660e\u3089\u304b\u3067\u3042\u308b\u3002\u3057\u304b\u3057\u3001\u9664\u6cd5\u306e\u64cd\u4f5c\u306b\u5bfe\u3057\u3066\u5546\u3068\u4f59\u308a\u3092\u898b\u3064\u3051\u308b\u3053\u3068\u306f\u53ef\u80fd\u3067\u3042\u308a\u3001\u5b9f\u969b<\/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\u500b\u306e\u7bb1\u306e\u96c6\u5408\u304c3\u500b\u305a\u3064\u306e\u30b0\u30eb\u30fc\u30d7\u306b\u5206\u3051\u3089\u308c\u3001\u305d\u306e\u7d50\u679c\u3068\u3057\u30665\u3064\u306e\u30b0\u30eb\u30fc\u30d7\u304c\u5f97\u3089\u308c\u30011\u3064\u304c\u4f59\u308b<\/figcaption><\/figure>\n<p>\u3057\u305f\u304c\u3063\u3066\u3001<span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">b=16<\/span><\/span> \u3092 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">a=3<\/span><\/span> \u3067\u5272\u308b\u3068\uff08\u3053\u3053\u3067 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">b<\/span><\/span> \u306f<strong>\u88ab\u9664\u6570<\/strong>\u3001<span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">a<\/span><\/span> \u306f<strong>\u9664\u6570<\/strong>\u3067\u3042\u308b\uff09\u3001<span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">16\/3<\/span><\/span> \u307e\u305f\u306f <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">16\\div 3<\/span><\/span> \u3068\u8868\u3055\u308c\u3001<strong>\u5546<\/strong>\u3068\u3057\u3066 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">q=5<\/span><\/span>\u3001<strong>\u4f59\u308a<\/strong>\u3068\u3057\u3066 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">r=1<\/span><\/span> \u304c\u5f97\u3089\u308c\u308b\u3002\u4e00\u822c\u306b\u3001<em>\u9664\u6cd5\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0<\/em>\u306f\u3001<span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">a\\neq 0<\/span><\/span> \u3092\u6e80\u305f\u3059\u4efb\u610f\u306e\u6574\u6570 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">a<\/span><\/span>\uff08\u9664\u6570\uff09\u304a\u3088\u3073 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">b<\/span><\/span>\uff08\u88ab\u9664\u6570\uff09\u306b\u5bfe\u3057\u3066\u3001\u6b21\u3092\u6e80\u305f\u3059\u4e00\u610f\u306a\u6574\u6570 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">q<\/span><\/span> \u3068 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">r<\/span><\/span> \u304c\u5b58\u5728\u3059\u308b\u3053\u3068\u3092\u4e3b\u5f35\u3059\u308b\u3002<\/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>\u3053\u306e\u4f8b\u3067\u306f <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">16=3\\cdot 5+1<\/span><\/span> \u3067\u3042\u308a\u3001\u6761\u4ef6 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">0\\le r&lt;|a|<\/span><\/span> \u306f <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">0\\le 1&lt;3<\/span><\/span> \u3067\u3042\u308b\u305f\u3081\u6e80\u305f\u3055\u308c\u3066\u3044\u308b\u3002\u3053\u306e\u5b9a\u5f0f\u5316\u306f\u3001\u9664\u6570\uff08\u307e\u305f\u306f\u88ab\u9664\u6570\uff09\u304c\u8ca0\u3067\u3042\u308a\u5f97\u308b\u5834\u5408\u306e\u66d6\u6627\u3055\u3092\u907f\u3051\u3001\u4f59\u308a\u304c\u5e38\u306b\u975e\u8ca0\u3067\u3042\u308a\u3001\u304b\u3064\u9664\u6570\u306e\u7d76\u5bfe\u5024\u3088\u308a\u53b3\u5bc6\u306b\u5c0f\u3055\u3044\u3053\u3068\u3092\u4fdd\u8a3c\u3059\u308b\u3002<\/p>\n<p><a name=\"2\"><\/a><\/p>\n<h2>\u30e6\u30fc\u30af\u30ea\u30c3\u30c9\u9664\u6cd5\u306e\u5b9a\u7406<\/h2>\n<p>\u9664\u6cd5\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u3092\u9069\u7528\u3057\u305f\u7d50\u679c\u306f\u3001<strong>\u30e6\u30fc\u30af\u30ea\u30c3\u30c9\u9664\u6cd5<\/strong>\u3068\u547c\u3070\u308c\u3001\u6b21\u306e\u7d50\u679c\u306b\u57fa\u3065\u3044\u3066\u3044\u308b\u3002<\/p>\n<p><b>\u5b9a\u7406\uff1a<\/b> <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">a,b\\in\\mathbb{Z}<\/span><\/span> \u3092 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">a\\neq 0<\/span><\/span> \u3068\u3059\u308b\u3002\u3053\u306e\u3068\u304d\u3001\u6b21\u3092\u6e80\u305f\u3059\u4e00\u610f\u306a <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">q,r\\in\\mathbb{Z}<\/span><\/span> \u304c\u5b58\u5728\u3059\u308b\u3002<\/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>\u6574\u6570 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">q<\/span><\/span> \u3092<strong>\u5546<\/strong>\u3001<span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">r<\/span><\/span> \u3092 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">b<\/span><\/span> \u3092 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">a<\/span><\/span> \u3067\u5272\u3063\u305f\u3068\u304d\u306e<strong>\u4f59\u308a<\/strong>\u3068\u547c\u3076\u3002<\/p>\n<p><a name=\"3\"><\/a><\/p>\n<h2>\u30e6\u30fc\u30af\u30ea\u30c3\u30c9\u9664\u6cd5\u306e\u8a3c\u660e<\/h2>\n<p>\u3053\u306e\u8a3c\u660e\u306f\u4e8c\u3064\u306e\u90e8\u5206\u306b\u5206\u304b\u308c\u308b\u3002\u307e\u305a\u5546\u3068\u4f59\u308a\u304c\u5b58\u5728\u3059\u308b\u3053\u3068\u3092\u793a\u3057\u3001\u6b21\u306b\u3001\u305d\u308c\u3089\u304c\u5b58\u5728\u3059\u308b\u3068\u3057\u3066\u4e00\u610f\u3067\u3042\u308b\u3053\u3068\u3092\u793a\u3059\u3002<\/p>\n<h3>\u5b58\u5728<\/h3>\n<p><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">a,b\\in\\mathbb{Z}<\/span><\/span> \u3092 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">a\\neq 0<\/span><\/span> \u3068\u3057\u3001<span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">d=|a|<\/span><\/span> \u3068\u5b9a\u7fa9\u3059\u308b\u3002\u3053\u306e\u3068\u304d <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">d&gt;0<\/span><\/span> \u3067\u3042\u308b\u3002\u307e\u305a <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">b\\ge 0<\/span><\/span> \u306e\u5834\u5408\u3092\u8a3c\u660e\u3059\u308b\u3002\u3059\u306a\u308f\u3061\u3001<span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">b=dq+r<\/span><\/span> \u304b\u3064 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">0\\le r&lt;d<\/span><\/span> \u3092\u6e80\u305f\u3059 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">q,r\\in\\mathbb{Z}<\/span><\/span> \u304c\u5b58\u5728\u3059\u308b\u3053\u3068\u3092\u793a\u3059\u3002\u6b21\u306b <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">b&lt;0<\/span><\/span> \u306e\u5834\u5408\u3092\u6271\u3046\u3002\u6700\u5f8c\u306b\u3001<span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">d<\/span><\/span> \u3092 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">|a|<\/span><\/span> \u306b\u7f6e\u304d\u63db\u3048\u308b\u3053\u3068\u3067\u3001<span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">0\\le r&lt;|a|<\/span><\/span> \u3092\u6e80\u305f\u3059\u5f62 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">b=qa+r<\/span><\/span> \u3092\u5f97\u308b\u3002<\/p>\n<p><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">b\\in\\mathbb{Z}<\/span><\/span> \u304b\u3064 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">b\\ge 0<\/span><\/span> \u3068\u3059\u308b\u3002\u3053\u306e\u3068\u304d\u547d\u984c <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">P(b)<\/span><\/span> \u3092\u6b21\u306e\u3088\u3046\u306b\u5b9a\u3081\u308b\u3002\u300c<span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">b=dq+r<\/span><\/span> \u304b\u3064 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">0\\le r&lt;d<\/span><\/span> \u3092\u6e80\u305f\u3059 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">q,r\\in\\mathbb{Z}<\/span><\/span> \u304c\u5b58\u5728\u3059\u308b\u300d\u3002<span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">P(b)<\/span><\/span> \u304c\u3059\u3079\u3066\u306e <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">b\\ge 0<\/span><\/span> \u306b\u5bfe\u3057\u3066\u6210\u308a\u7acb\u3064\u3053\u3068\u3092\u3001\u6570\u5b66\u7684\u5e30\u7d0d\u6cd5\u306b\u3088\u3063\u3066\u793a\u3059\u3002<\/p>\n<p><strong>\u57fa\u5e95\u306e\u5834\u5408\uff1a<\/strong> <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">b=0<\/span><\/span> \u306e\u3068\u304d\u3001<span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">q=0<\/span><\/span> \u304a\u3088\u3073 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">r=0<\/span><\/span> \u3068\u53d6\u308c\u3070\u3001<span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">0=d\\cdot 0+0<\/span><\/span> \u304b\u3064 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">0\\le 0&lt;d<\/span><\/span> \u304c\u5f97\u3089\u308c\u308b\u3002\u3057\u305f\u304c\u3063\u3066 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">P(0)<\/span><\/span> \u306f\u771f\u3067\u3042\u308b\u3002<\/p>\n<p><strong>\u5e30\u7d0d\u6bb5\u968e\uff1a<\/strong> <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">k\\ge 0<\/span><\/span> \u3068\u3057\u3001<span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">P(k)<\/span><\/span> \u304c\u771f\u3067\u3042\u308b\u3068\u4eee\u5b9a\u3059\u308b\u3002\u3053\u306e\u3068\u304d\u3001\u6b21\u3092\u6e80\u305f\u3059 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">q,r\\in\\mathbb{Z}<\/span><\/span> \u304c\u5b58\u5728\u3059\u308b\u3002<\/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>\u4e21\u8fba\u306b <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">1<\/span><\/span> \u3092\u52a0\u3048\u308b\u3068<\/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>\u3055\u3089\u306b <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">0\\le r&lt;d<\/span><\/span> \u304b\u3089 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">r+1\\le d<\/span><\/span> \u304c\u5f93\u3046\u3002\u3057\u305f\u304c\u3063\u3066\u3001<span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">r+1&lt;d<\/span><\/span> \u307e\u305f\u306f <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">r+1=d<\/span><\/span> \u306e\u3044\u305a\u308c\u304b\u306e\u5834\u5408\u306e\u307f\u304c\u8d77\u3053\u308a\u5f97\u308b\u3002<\/p>\n<p><b>\u5834\u54081\uff1a<\/b> <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">r+1&lt;d<\/span><\/span> \u306e\u3068\u304d\u3001<span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">q&#039;=q<\/span><\/span> \u304a\u3088\u3073 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">r&#039;=r+1<\/span><\/span> \u3068\u5b9a\u3081\u308b\u3002\u3053\u306e\u3068\u304d<\/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>\u5834\u54082\uff1a<\/b> <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">r+1=d<\/span><\/span> \u306e\u3068\u304d\u3001<span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">k+1=dq+d=d(q+1)+0<\/span><\/span> \u3068\u306a\u308b\u3002<span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">q&#039;=q+1<\/span><\/span> \u304a\u3088\u3073 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">r&#039;=0<\/span><\/span> \u3068\u5b9a\u3081\u308c\u3070\u3001<\/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>\u3044\u305a\u308c\u306e\u5834\u5408\u306b\u304a\u3044\u3066\u3082\u3001<span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">k+1=dq&#039;+r&#039;<\/span><\/span> \u304b\u3064 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">0\\le r&#039;&lt;d<\/span><\/span> \u3092\u6e80\u305f\u3059\u6574\u6570 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">q&#039;,r&#039;<\/span><\/span> \u3092\u69cb\u6210\u3067\u304d\u305f\u3002\u3057\u305f\u304c\u3063\u3066 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">P(k+1)<\/span><\/span> \u306f\u771f\u3067\u3042\u308b\u3002\u4ee5\u4e0a\u3088\u308a\u3001\u5e30\u7d0d\u6cd5\u306b\u3088\u3063\u3066 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">P(b)<\/span><\/span> \u306f\u3059\u3079\u3066\u306e <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">b\\ge 0<\/span><\/span> \u306b\u5bfe\u3057\u3066\u6210\u308a\u7acb\u3064\u3002<\/p>\n<p>\u6b21\u306b <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">b&lt;0<\/span><\/span> \u306e\u5834\u5408\u3092\u8003\u3048\u308b\u3002\u3053\u306e\u3068\u304d <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">-b&gt;0<\/span><\/span> \u3067\u3042\u308b\u3002\u524d\u306e\u7d50\u679c\u3092 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">-b<\/span><\/span> \u306b\u9069\u7528\u3059\u308b\u3068\u3001\u6b21\u3092\u6e80\u305f\u3059 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">q,r\\in\\mathbb{Z}<\/span><\/span> \u304c\u5b58\u5728\u3059\u308b\u3002<\/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>\u4e21\u8fba\u306b <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">-1<\/span><\/span> \u3092\u639b\u3051\u308b\u3068<\/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><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">r=0<\/span><\/span> \u306e\u5834\u5408\u3001<span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">q_1=-q<\/span><\/span> \u304a\u3088\u3073 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">r_1=0<\/span><\/span> \u3068\u53d6\u308c\u3070\u3001<span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">b=dq_1+r_1<\/span><\/span> \u304b\u3064 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">0\\le r_1&lt;d<\/span><\/span> \u304c\u6210\u308a\u7acb\u3064\u3002<\/p>\n<p><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">r&gt;0<\/span><\/span> \u306e\u5834\u5408\u3001<span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">q_1=-q-1<\/span><\/span> \u304a\u3088\u3073 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">r_1=d-r<\/span><\/span> \u3068\u5b9a\u3081\u308b\u3002<span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">0&lt;r&lt;d<\/span><\/span> \u3067\u3042\u308b\u304b\u3089\u3001<span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">0&lt;d-r&lt;d<\/span><\/span>\u3001\u3059\u306a\u308f\u3061 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">0\\le r_1&lt;d<\/span><\/span> \u304c\u6210\u308a\u7acb\u3064\u3002\u3055\u3089\u306b\u3001<\/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>\u3057\u305f\u304c\u3063\u3066\u3001\u3059\u3079\u3066\u306e <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">b\\in\\mathbb{Z}<\/span><\/span> \u306b\u5bfe\u3057\u3066\u3001<span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">b=dq_1+r_1<\/span><\/span> \u304b\u3064 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">0\\le r_1&lt;d<\/span><\/span> \u3092\u6e80\u305f\u3059 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">q_1,r_1\\in\\mathbb{Z}<\/span><\/span> \u304c\u5b58\u5728\u3059\u308b\u3002<\/p>\n<p>\u6700\u5f8c\u306b\u3001<span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">d=|a|<\/span><\/span> \u3067\u3042\u308b\u3053\u3068\u3092\u601d\u3044\u51fa\u305d\u3046\u3002<span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">a&gt;0<\/span><\/span> \u306e\u3068\u304d\u3001<span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">d=a<\/span><\/span> \u3067\u3042\u308a\u3001\u7b49\u5f0f <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">b=dq_1+r_1<\/span><\/span> \u306f <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">b=aq_1+r_1<\/span><\/span> \u3068\u66f8\u3051\u3001<span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">0\\le r_1&lt;|a|<\/span><\/span> \u3092\u6e80\u305f\u3059\u3002<\/p>\n<p><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">a&lt;0<\/span><\/span> \u306e\u3068\u304d\u3001<span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">d=-a<\/span><\/span> \u3067\u3042\u308a\u3001<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> \u3068\u306a\u308b\u3002<span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">q=-q_1<\/span><\/span> \u304a\u3088\u3073 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">r=r_1<\/span><\/span> \u3068\u5b9a\u7fa9\u3059\u308b\u3068\u3001\u6b21\u3092\u5f97\u308b\u3002<\/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>\u3053\u308c\u306b\u3088\u308a\u3001<span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">a\\neq 0<\/span><\/span> \u3092\u6e80\u305f\u3059\u4efb\u610f\u306e <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">a,b\\in\\mathbb{Z}<\/span><\/span> \u306b\u5bfe\u3057\u3066\u3001<span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">q<\/span><\/span> \u304a\u3088\u3073 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">r<\/span><\/span> \u306e\u5b58\u5728\u304c\u793a\u3055\u308c\u305f\u3002<\/p>\n<h3>\u4e00\u610f\u6027<\/h3>\n<p><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">q,q&#039;,r,r&#039;\\in\\mathbb{Z}<\/span><\/span> \u304c\u5b58\u5728\u3057\u3066\u3001\u6b21\u304c\u6210\u308a\u7acb\u3064\u3068\u4eee\u5b9a\u3059\u308b\u3002<\/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>\u4e21\u5f0f\u3092\u6e1b\u305a\u308b\u3068\u3001<\/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><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">0\\le r,r&#039;&lt;|a|<\/span><\/span> \u3067\u3042\u308b\u304b\u3089\u3001<span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">|r&#039;-r|&lt;|a|<\/span><\/span> \u304c\u6210\u308a\u7acb\u3064\u3002\u4e00\u65b9\u3001\u5de6\u8fba\u306f <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">a<\/span><\/span> \u306e\u500d\u6570\u3067\u3042\u308a\u3001\u3057\u305f\u304c\u3063\u3066 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">|a|<\/span><\/span> \u306e\u500d\u6570\u3067\u3082\u3042\u308b\u3002\u7d76\u5bfe\u5024\u304c <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">|a|<\/span><\/span> \u3088\u308a\u53b3\u5bc6\u306b\u5c0f\u3055\u3044 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">|a|<\/span><\/span> \u306e\u6574\u6570\u500d\u306f <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">0<\/span><\/span> \u306e\u307f\u3067\u3042\u308b\u3002\u5b9f\u969b\u3001<span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">m\\in\\mathbb{Z}<\/span><\/span> \u3067 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">|a| m \\neq 0<\/span><\/span> \u306a\u3089\u3070\u3001<span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\big| |a| m \\big| \\ge |a| <\/span><\/span> \u3068\u306a\u308b\u3002\u3057\u305f\u304c\u3063\u3066 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">r&#039;-r=0<\/span><\/span>\u3001\u3059\u306a\u308f\u3061 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">r=r&#039;<\/span><\/span> \u3067\u3042\u308a\u3001\u3053\u308c\u3092 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">b=qa+r<\/span><\/span> \u306b\u4ee3\u5165\u3059\u308b\u3068 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">q=q&#039;<\/span><\/span> \u304c\u5f93\u3046\u3002\u3086\u3048\u306b\u3001\u3053\u306e\u5206\u89e3\u306f\u4e00\u610f\u3067\u3042\u308b\u3002<\/p>\n<p><a name=\"4\"><\/a><\/p>\n<h2>\u5546\u3068\u4f59\u308a\u306e\u89e3\u91c8<\/h2>\n<ul>\n<li style=\"text-align: justify;\">\n    <strong>\u300c\u4f59\u308a\u300d\u3068\u306f\u4f55\u304b\u3002<\/strong> <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">b=qa+r<\/span><\/span> \u306e\u3068\u304d\u3001<span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">r=b-qa<\/span><\/span> \u306f <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">b<\/span><\/span> \u304b\u3089\u500d\u6570 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">qa<\/span><\/span> \u3092\u53d6\u308a\u9664\u3044\u305f\u3068\u304d\u306b\u300c\u6b8b\u308b\u300d\u3082\u306e\u3067\u3042\u308b\u3002\u8a00\u3044\u63db\u3048\u308c\u3070\u3001<span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">r<\/span><\/span> \u306f <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">a<\/span><\/span> \u306e\u500d\u6570\u306e\u683c\u5b50\u306b <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">b<\/span><\/span> \u3092\u5408\u308f\u305b\u305f\u3068\u304d\u306e\u5270\u4f59\u3067\u3042\u308b\u3002\n  <\/li>\n<li style=\"text-align: justify;\">\n    <strong>\u306a\u305c<\/strong> <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">0\\le r&lt;|a|<\/span><\/span> <strong>\u3092\u8981\u6c42\u3059\u308b\u306e\u304b\u3002<\/strong> \u3053\u306e\u6761\u4ef6\u304c\u306a\u3051\u308c\u3070\u3001\u7d44 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">(q,r)<\/span><\/span> \u306f\u4e00\u610f\u3067\u306f\u306a\u3044\u3002\u5b9f\u969b\u3001<span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">b=qa+r<\/span><\/span> \u306a\u3089\u3070\u3001<span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">b=a(q+1)+(r-a)<\/span><\/span> \u3082\u6210\u308a\u7acb\u3064\u3002\u6761\u4ef6 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">0\\le r&lt;|a|<\/span><\/span> \u306f\u3001\u4f59\u308a\u3092\u56fa\u5b9a\u3055\u308c\u305f\u533a\u9593 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\{0,1,2,\\dots,|a|-1\\}<\/span><\/span> \u306b\u5236\u9650\u3057\u3001\u540c\u3058\u6570\u306b\u5bfe\u3059\u308b\u7121\u9650\u500b\u306e\u300c\u518d\u30e9\u30d9\u30eb\u4ed8\u3051\u300d\u3092\u9632\u3050\u3002\n  <\/li>\n<li style=\"text-align: justify;\">\n    <strong><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">a<\/span><\/span> \u304c\u8ca0\u306e\u5834\u5408\u306f\u3069\u3046\u306a\u308b\u304b\u3002<\/strong> \u5b9a\u7406\u306f\u5909\u66f4\u306a\u304f\u6210\u308a\u7acb\u3061\u3001\u4f59\u308a\u306f\u975e\u8ca0\u3067 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">|a|<\/span><\/span> \u306b\u3088\u3063\u3066\u4e0a\u304b\u3089\u6291\u3048\u3089\u308c\u308b\u3002\u3053\u308c\u306f\u3001\u3044\u304f\u3064\u304b\u306e\u30d7\u30ed\u30b0\u30e9\u30df\u30f3\u30b0\u8a00\u8a9e\u304c\u30bc\u30ed\u65b9\u5411\u3078\u306e\u5207\u308a\u6368\u3066\u3092\u7528\u3044\u3001\u8ca0\u306e\u4f59\u308a\u3092\u751f\u6210\u3059\u308b\u5834\u5408\u304c\u3042\u308b\u306e\u306b\u5bfe\u3057\u3001\u6570\u5b66\u3067\u306f\u4f59\u308a\u3092\u300c\u6a19\u6e96\u7684\u300d\u306a\u4ee3\u8868\u3068\u3059\u308b\u305f\u3081\u306b <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">0\\le r&lt;|a|<\/span><\/span> \u306e\u898f\u7d04\u3092\u63a1\u7528\u3059\u308b\u70b9\u3067\u91cd\u8981\u3067\u3042\u308b\u3002<\/p>\n<p>    \u3055\u3089\u306b\u3001<span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">a&gt;0<\/span><\/span> \u306e\u3068\u304d\u3001\u5546\u306f\u5e8a\u95a2\u6570\u306b\u4e00\u81f4\u3059\u308b\u3002<\/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>\u7b46\u7b97\u306b\u3088\u308b\u9664\u6cd5\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0<\/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>\u30e6\u30fc\u30af\u30ea\u30c3\u30c9\u9664\u6cd5\u306b\u57fa\u3065\u3044\u3066\u3001\u6570\u306e\u4f4d\u53d6\u308a\u8868\u73fe\u3092\u5229\u7528\u3059\u308b\u3053\u3068\u3067\u3001\u7b46\u7b97\u306b\u3088\u308b\u9664\u6cd5\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u3092\u5b9f\u88c5\u3059\u308b\u3053\u3068\u304c\u3067\u304d\u308b\u3002\u3053\u306e\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306f\u3001<span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">a,b\\in\\mathbb{Z}<\/span><\/span> \u304b\u3064 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">a\\neq 0<\/span><\/span> \u306e\u3082\u3068\u3067 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">b\\div a<\/span><\/span> \u3092\u8a08\u7b97\u3057\u305f\u3044\u3068\u304d\u306b\u3001<span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">q<\/span><\/span> \u3068 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">r<\/span><\/span> \u306e\u5024\u3092\u8fc5\u901f\u306b\u6c42\u3081\u308b\u3053\u3068\u3092\u53ef\u80fd\u306b\u3059\u308b\u8a08\u7b97\u6280\u6cd5\u3067\u3042\u308b\u3002<\/p>\n<p>\u3053\u308c\u3092\u8aac\u660e\u3059\u308b\u305f\u3081\u306b\u3001\u307e\u305a\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306e\u5b9f\u884c\u904e\u7a0b\u304a\u3088\u3073\u8d77\u3053\u308a\u5f97\u308b\u72b6\u6cc1\u3092\u793a\u3059\u3044\u304f\u3064\u304b\u306e\u4f8b\u3092\u78ba\u8a8d\u3057\u3088\u3046\u3002<\/p>\n<ol>\n<li>\n<p><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">57\\div 4<\/span><\/span> \u3092\u8a08\u7b97\u3057\u305f\u3044\u3068\u4eee\u5b9a\u3059\u308b\u3002\u3053\u3053\u3067 57 \u306f<strong>\u88ab\u9664\u6570<\/strong>\u30014 \u306f<strong>\u9664\u6570<\/strong>\u3067\u3042\u308b\u3002\u3053\u308c\u3092\u884c\u3046\u305f\u3081\u306b\u3001\u6b21\u306e\u8a08\u7b97\u624b\u9806\u3092\u5b9f\u884c\u3059\u308b\u3002<\/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{\u9664\u6cd5\u306e\u6f14\u7b97\u3092\u66f8\u304f\u3002} \\\\ \\\\\n\n(2) &amp; \\color{red}5&#039;\\color{black}7 \\div 4 =  \\\\ &amp; \\text{\u88ab\u9664\u6570\u306e\u5de6\u304b\u3089\u3001\u9664\u6570\u4ee5\u4e0a\u3068\u306a\u308b\u6700\u521d\u306e\u63a5\u982d\u90e8\u5206\u3092}\\\\\n\n&amp;\\text{\u5206\u96e2\u3059\u308b\u3002\u3053\u306e\u5834\u5408\u306f 5 \u3067\u3042\u308b\u3002} \\\\ \\\\\n\n(3) &amp; 5&#039;7 \\div 4 = \\color{red}1\\color{black} \\\\ &amp; \\text{$4$ \u3092\u639b\u3051\u3066 $5$ \u4ee5\u4e0b\u3068\u306a\u308b\u6700\u5927\u306e\u6570\u3092\u8003\u3048\u3001}\\\\\n\n&amp;\\text{\u305d\u308c\u3092\u7b49\u53f7\u306e\u53f3\u306b\u66f8\u304f\u3002\u3053\u308c\u306f 1 \u3067\u3042\u308b\u3002} \\\\ \\\\\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{\u7d50\u679c\u3092\u9664\u6570\u3067\u639b\u3051\u3001\u9078\u629e\u3057\u305f\u5024\u304b\u3089\u5f15\u304f\u3002} \\\\ \\\\\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{\u6b21\u306e\u6841\u3092\u9078\u629e\u3057\u3066\u300c\u4e0b\u308d\u3059\u300d\u3002} \\\\ \\\\\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{\u5f97\u3089\u308c\u305f\u6700\u5f8c\u306e\u6570\u3067\u540c\u3058\u624b\u9806\u3092\u7e70\u308a\u8fd4\u3059\u3002}\n\n\\end{array}\n\n<\/span>\n<p>\u300c\u4e0b\u308d\u3059\u300d\u6841\u304c\u5c3d\u304d\u305f\u6642\u70b9\u3067\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306f\u7d42\u4e86\u3057\u3001\u7d50\u679c\u3068\u3057\u3066\u5546 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">q=14<\/span><\/span>\u3001\u4f59\u308a <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">r=1<\/span><\/span> \u304c\u5f97\u3089\u308c\u308b\u3002\u7279\u306b\u3001\u4f59\u308a\u306f\u5e38\u306b\u9664\u6570\u3088\u308a\u5c0f\u3055\u304f\u306a\u308b\u3002<\/p>\n<\/li>\n<li>\n<p><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">132\\div 5<\/span><\/span> \u3092\u8a08\u7b97\u3057\u305f\u3044\u3068\u4eee\u5b9a\u3059\u308b\u3002\u3053\u306e\u5834\u5408\u3001\u6b21\u306e\u8a08\u7b97\u624b\u9806\u3092\u5b9f\u884c\u3059\u308b\u3002<\/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{\u88ab\u9664\u6570\u306e\u6700\u521d\u306e\u63a5\u982d\u90e8\u5206\u3092\u5206\u96e2\u3057\u3001}\\\\\n\n&amp; \\text{5 \u3092\u639b\u3051\u3066\u305d\u308c\u4ee5\u4e0b\u3068\u306a\u308b\u81ea\u7136\u6570\u3092\u63a2\u3059\u3002}\\\\\n\n&amp; \\text{\u3067\u304d\u306a\u3044\u5834\u5408\u306f\u3001\u53ef\u80fd\u306b\u306a\u308b\u307e\u3067\u6b21\u306e\u6841\u3092\u52a0\u3048\u308b\u3002} \\\\ \\\\\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{\u524d\u306e\u6bb5\u968e\u304c\u6210\u7acb\u3057\u305f\u3089\u3001\u901a\u5e38\u3069\u304a\u308a\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u3092\u5b9f\u884c\u3059\u308b\u3002} \\\\ \\\\\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>\u88ab\u9664\u6570\u306e\u6841\u6570\u304c\u591a\u3044\u5834\u5408\u3082\u3001\u624b\u9806\u306f\u540c\u69d8\u306b\u5b9f\u884c\u3055\u308c\u308b\u3002\u4f8b\u3048\u3070\u3001<span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">3521\\div 12<\/span><\/span> \u3092\u8a08\u7b97\u3059\u308b\u3068\u3001\u6b21\u304c\u5f97\u3089\u308c\u308b\u3002<\/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>\u3044\u305a\u308c\u304b\u306e\u6570\u304c\u8ca0\u3067\u3042\u308b\u5834\u5408\u3001\u7d50\u679c\u306e\u8868\u3057\u65b9\u306b\u306f\u4e8c\u3064\u306e\u8a31\u5bb9\u3055\u308c\u308b\u5f62\u5f0f\u304c\u5b58\u5728\u3059\u308b\u3002\u305f\u3060\u3057\u3001\u6570\u8ad6\u306b\u304a\u3051\u308b\u6a19\u6e96\u7684\u306a\u5f62\u5f0f\u306f\u3001\u4f59\u308a\u304c\u6b63\u3067\u3042\u308a\u3001\u30e6\u30fc\u30af\u30ea\u30c3\u30c9\u9664\u6cd5\u3068\u6574\u5408\u7684\u306a\u3082\u306e\u3067\u3042\u308b\u3002\u4f8b\u3048\u3070\u3001<span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">-598\\div 21<\/span><\/span> \u3092\u8a08\u7b97\u3059\u308b\u3068\u3001\u6b21\u306e\u4e8c\u3064\u306e\u5c55\u958b\u304c\u5f97\u3089\u308c\u3001\u3044\u305a\u308c\u3082\u6052\u7b49\u5f0f\u3068\u3057\u3066\u6b63\u3057\u3044\u3002<\/p>\n<ul>\n<li>\n        <b>\u8ca0\u306e\u4f59\u308a\u3092\u7528\u3044\u308b\u5834\u5408\uff1a<\/b> \u3053\u308c\u306f\u3001\u8a08\u7b97\u306e\u521d\u3081\u306b\u7b26\u53f7\u3092\u9664\u304d\u3001\u6700\u5f8c\u306b\u305d\u308c\u3092\u623b\u3059\u3053\u3068\u3067\u5f97\u3089\u308c\u308b\u3002<\/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>\u3053\u3053\u304b\u3089\u6b21\u304c\u5f97\u3089\u308c\u308b\u3002<\/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>\u6b21\u306b\u3001\u3053\u306e\u7b49\u5f0f\u5168\u4f53\u3092 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">-1<\/span><\/span> \u500d\u3059\u308b\u3068\u3001<\/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>\u3057\u305f\u304c\u3063\u3066\u3001\u3053\u306e\u8868\u73fe\u3067\u306f <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">-598\\div 21<\/span><\/span> \u306e\u7d50\u679c\u306f\u3001\u5546 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">q=-28<\/span><\/span>\u3001\u4f59\u308a <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">r=-10<\/span><\/span> \u3068\u306a\u308b\u3002<\/p>\n<p>\u3055\u3089\u306b\u3001\u7b49\u5f0f\u5168\u4f53\u3092\u518d\u3073 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">-1<\/span><\/span> \u500d\u3059\u308b\u3068\u3001<\/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>\u3057\u305f\u304c\u3063\u3066\u3001<span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">598\\div (-21)<\/span><\/span> \u306e\u7d50\u679c\u306f\u3001\u5546 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">q=-28<\/span><\/span>\u3001\u4f59\u308a <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">r=10<\/span><\/span> \u3067\u3042\u308b\u3002<\/p>\n<\/li>\n<li>\n        <b>\u6b63\u306e\u4f59\u308a\u3092\u7528\u3044\u3001\u30e6\u30fc\u30af\u30ea\u30c3\u30c9\u9664\u6cd5\u3068\u6574\u5408\u7684\u306a\u5834\u5408\uff1a<\/b> \u524d\u306e\u5c55\u958b\u304b\u3089\u6b21\u304c\u5f97\u3089\u308c\u308b\u3002<\/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>\u6b21\u306b\u3001\u3053\u306e\u7b49\u5f0f\u306e\u53f3\u8fba\u306b <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">0=21-21<\/span><\/span> \u3092\u52a0\u3048\u308b\u3068\u3001<\/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>\u3057\u305f\u304c\u3063\u3066\u3001\u30e6\u30fc\u30af\u30ea\u30c3\u30c9\u9664\u6cd5\u3068\u6574\u5408\u7684\u306b\u8003\u3048\u308b\u3068\u3001<span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">-598\\div 21<\/span><\/span> \u306e\u7d50\u679c\u306f\u3001\u5546 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">q=-29<\/span><\/span>\u3001\u4f59\u308a <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">r=11<\/span><\/span> \u3068\u306a\u308b\u3002<\/p>\n<\/li>\n<\/ul>\n<p>\u30e6\u30fc\u30af\u30ea\u30c3\u30c9\u9664\u6cd5\u306b\u304a\u3051\u308b\u6163\u7fd2\u306b\u95a2\u3057\u3066\u306f\u3001\u6b63\u306e\u4f59\u308a\u3092\u3082\u3064\u7d50\u679c\u306e\u307f\u304c\u30e6\u30fc\u30af\u30ea\u30c3\u30c9\u7684\u306a\u5546\u3068\u4f59\u308a\u306b\u5bfe\u5fdc\u3059\u308b\u3002\u3057\u304b\u3057\u3001\u3044\u305a\u308c\u306e\u8868\u73fe\u3082\u6b63\u3057\u3044\u6052\u7b49\u5f0f\u3067\u3042\u308a\u3001\u7570\u306a\u308b\u6587\u8108\u3067\u306f\u6709\u7528\u3068\u306a\u308a\u5f97\u308b\u3002\u7b46\u7b97\u306b\u3088\u308b\u9664\u6cd5\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306f\u8ca0\u306e\u4f59\u308a\u3092\u751f\u3058\u308b\u3053\u3068\u304c\u3042\u308b\u304c\u3001\u3053\u308c\u306f\u6a5f\u68b0\u7684\u306b\u7d50\u679c\u3092\u5f97\u305f\u308a\u3001\u8ffd\u52a0\u306e\u624b\u9806\u306a\u3057\u306b\u4ee3\u6570\u7684\u64cd\u4f5c\u3092\u884c\u3063\u305f\u308a\u3059\u308b\u3046\u3048\u3067\u5b9f\u7528\u7684\u3067\u3042\u308b\u3002\u4e00\u65b9\u3001\u30e6\u30fc\u30af\u30ea\u30c3\u30c9\u9664\u6cd5\u3068\u6574\u5408\u7684\u306a\u6b63\u306e\u4f59\u308a\u3092\u3082\u3064\u7d50\u679c\u306f\u3001\u5404\u5270\u4f59\u985e\u306e\u6a19\u6e96\u7684\uff08\u30ab\u30ce\u30cb\u30ab\u30eb\uff09\u306a\u4ee3\u8868\uff08\u4f8b\u3048\u3070 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\{0,1,\\dots,n-1\\}<\/span><\/span>\uff09\u3092\u5b9a\u3081\u308b\u3053\u3068\u3092\u53ef\u80fd\u306b\u3057\u3001\u6574\u6570\u3092\u6b63\u78ba\u304b\u3064\u66d6\u6627\u3055\u306a\u304f\u30e9\u30d9\u30eb\u4ed8\u3051\u3059\u308b\u3053\u3068\u3092\u5bb9\u6613\u306b\u3059\u308b\u3002\u306a\u304a\u3001\u5bfe\u79f0\u5270\u4f59\u306a\u3069\u3001\u898f\u5247\u3092\u56fa\u5b9a\u3059\u308c\u3070\u540c\u69d8\u306b\u6709\u52b9\u306a\u4ed6\u306e\u4ee3\u8868\u306e\u53d6\u308a\u65b9\u3082\u5b58\u5728\u3059\u308b\u3002<\/p>\n<\/li>\n<\/ol>\n<p><a name=\"6\"><\/a><\/p>\n<h2>\u7d50\u8ad6<\/h2>\n<p>\u9664\u6cd5\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306f\u3001\u4efb\u610f\u306e\u6574\u6570\u9664\u6cd5\u304c\u4e00\u610f\u306b <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">b=qa+r<\/span><\/span>\uff08<span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">0\\le r&lt;|a|<\/span><\/span>\uff09\u306e\u5f62\u3067\u8868\u3055\u308c\u308b\u3053\u3068\u3092\u4fdd\u8a3c\u3057\u3001\u8ca0\u306e\u6570\u304c\u95a2\u4e0e\u3059\u308b\u5834\u5408\u3067\u3042\u3063\u3066\u3082\u5546\u3068\u4f59\u308a\u3092\u89e3\u91c8\u3059\u308b\u305f\u3081\u306e\u6a19\u6e96\u7684\u306a\u57fa\u6e96\u3092\u4e0e\u3048\u308b\u3002\u7b46\u7b97\u306b\u3088\u308b\u9664\u6cd5\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306f\u3001\u3053\u306e\u5206\u89e3\u3092\u4f4d\u53d6\u308a\u8868\u73fe\u306b\u57fa\u3065\u3044\u3066\u5b9f\u88c5\u3057\u305f\u5b9f\u7528\u7684\u624b\u7d9a\u304d\u306b\u904e\u304e\u305a\u3001<span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">q<\/span><\/span> \u3068 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">r<\/span><\/span> \u3092\u6a5f\u68b0\u7684\u306b\u8a08\u7b97\u3059\u308b\u3053\u3068\u3092\u53ef\u80fd\u306b\u3059\u308b\u3002\u6700\u5f8c\u306b\u3001\u3053\u306e\u30e6\u30fc\u30af\u30ea\u30c3\u30c9\u7684\u5f62\u5f0f\u306f\u66d6\u6627\u3055\u3092\u56de\u907f\u3059\u308b\u3060\u3051\u3067\u306a\u304f\u3001\u5408\u540c\u7b97\u8853\u3068\u3082\u81ea\u7136\u306b\u7d50\u3073\u4ed8\u304f\u3002\u3059\u306a\u308f\u3061\u3001\u4f59\u308a <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">r<\/span><\/span> \u306f\u3001\u6cd5 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">a<\/span><\/span> \u306b\u3088\u308b <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">b<\/span><\/span> \u306e\u5270\u4f59\u985e\u306e\u6a19\u6e96\u7684\u4ee3\u8868\u3068\u3057\u3066\u6a5f\u80fd\u3057\u3001\u6570\u8ad6\u306b\u304a\u3051\u308b\u591a\u304f\u306e\u624b\u6cd5\u3084\u8a08\u7b97\u6a5f\u5fdc\u7528\u306e\u57fa\u76e4\u3068\u306a\u308b\u3002\u3053\u308c\u3089\u306f\u4eca\u5f8c\u306e\u56de\u3067\u691c\u8a0e\u3055\u308c\u308b\u4e88\u5b9a\u3067\u3042\u308b\u3002<\/p>\n<p><a name=\"7\"><\/a><\/p>\n<h2>\u63d0\u6848\u304a\u3088\u3073\u89e3\u7b54\u4ed8\u304d\u6f14\u7fd2<\/h2>\n<h3>\u30e6\u30fc\u30af\u30ea\u30c3\u30c9\u9664\u6cd5<\/h3>\n<ol>\n<li><strong>\uff08\u89e3\u7b54\u6e08\u307f\uff09<\/strong> \u6b21\u3092\u6e80\u305f\u3059 <span class=\"katex-eq\" data-katex-display=\"false\">q<\/span> \u3068 <span class=\"katex-eq\" data-katex-display=\"false\">r<\/span> \u3092\u6c42\u3081\u3088\u3002\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>\u89e3\u7b54\uff1a<\/strong> <span class=\"katex-eq\" data-katex-display=\"false\">9<\/span> \u3092\u639b\u3051\u3066\u3082 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">137<\/span><\/span> \u3092\u8d85\u3048\u306a\u3044\u6700\u5927\u306e\u6570\u3092\u63a2\u3059\u3002<span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">15\\times 9 = 135<\/span><\/span> \u3067\u3042\u308a\u3001<span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">16\\times 9 = 144<\/span><\/span> \u3067\u3042\u308b\u304b\u3089\u3001\u6c42\u3081\u308b\u5546\u306f <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">q=15<\/span><\/span> \u3067\u3042\u308b\u3002\u6b21\u306b\u4f59\u308a <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">r=137-9q<\/span><\/span> \u3092\u8a08\u7b97\u3057\u3001<span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">0\\le r\\lt 9<\/span><\/span> \u3092\u78ba\u8a8d\u3059\u308b\u3002\u8a08\u7b97\u3059\u308b\u3068\u6b21\u3092\u5f97\u308b\u3002<\/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>\u3057\u305f\u304c\u3063\u3066\u3001<span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">137=9\\cdot 15+2<\/span><\/span> \u304b\u3064 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">0\\le 2\\lt 9<\/span><\/span> \u3067\u3042\u308b\u3002<\/p>\n<\/li>\n<li><strong>\uff08\u89e3\u7b54\u6e08\u307f\uff09<\/strong> \u6b21\u3092\u6e80\u305f\u3059 <span class=\"katex-eq\" data-katex-display=\"false\">q<\/span> \u3068 <span class=\"katex-eq\" data-katex-display=\"false\">r<\/span> \u3092\u6c42\u3081\u3088\u3002\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>\u89e3\u7b54\uff1a<\/strong> <span class=\"katex-eq\" data-katex-display=\"false\">37<\/span> \u3092\u639b\u3051\u3066\u3082 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">2025<\/span><\/span> \u3092\u8d85\u3048\u306a\u3044\u6700\u5927\u306e\u6570\u3092\u63a2\u3059\u3002<span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">37\\times 54 = 1998<\/span><\/span>\u3001<span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">37\\times 55 = 2035<\/span><\/span> \u3067\u3042\u308b\u304b\u3089\u3001\u6c42\u3081\u308b\u5546\u306f <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">q=54<\/span><\/span> \u3067\u3042\u308b\u3002\u6b21\u306b\u4f59\u308a <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">r=2025-37q<\/span><\/span> \u3092\u8a08\u7b97\u3057\u3001<span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">0\\le r\\lt 37<\/span><\/span> \u3092\u78ba\u8a8d\u3059\u308b\u3002\u8a08\u7b97\u3059\u308b\u3068\u6b21\u3092\u5f97\u308b\u3002<\/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>\u3057\u305f\u304c\u3063\u3066\u3001<span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">2025=37\\cdot 54+27<\/span><\/span> \u304b\u3064 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">0\\le 27\\lt 37<\/span><\/span> \u3067\u3042\u308b\u3002<\/p>\n<\/li>\n<li>\u6b21\u3092\u6e80\u305f\u3059 <span class=\"katex-eq\" data-katex-display=\"false\">q<\/span> \u3068 <span class=\"katex-eq\" data-katex-display=\"false\">r<\/span> \u3092\u6c42\u3081\u3088\u3002\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>\u6b21\u3092\u6e80\u305f\u3059 <span class=\"katex-eq\" data-katex-display=\"false\">q<\/span> \u3068 <span class=\"katex-eq\" data-katex-display=\"false\">r<\/span> \u3092\u6c42\u3081\u3088\u3002\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>\u6b21\u3092\u6e80\u305f\u3059 <span class=\"katex-eq\" data-katex-display=\"false\">q<\/span> \u3068 <span class=\"katex-eq\" data-katex-display=\"false\">r<\/span> \u3092\u6c42\u3081\u3088\u3002\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>\u4f59\u308a\u3092\u56fa\u5b9a\u3057\u305f\u6574\u6570\u306e\u63a2\u7d22\u3002<\/strong> <span class=\"katex-eq\" data-katex-display=\"false\">a=12<\/span> \u3068\u3059\u308b\u3002\n<p>(a) <span class=\"katex-eq\" data-katex-display=\"false\">12<\/span> \u306b\u3088\u308b\u30e6\u30fc\u30af\u30ea\u30c3\u30c9\u9664\u6cd5\u306e\u4f59\u308a\u304c <span class=\"katex-eq\" data-katex-display=\"false\">r=5<\/span> \u3068\u306a\u308b\u3059\u3079\u3066\u306e\u6574\u6570 <span class=\"katex-eq\" data-katex-display=\"false\">b<\/span> \u306e\u96c6\u5408\u3092\u8a18\u8ff0\u305b\u3088\u3002<\/p>\n<p>(b) \u4e0a\u8a18\u3092\u6e80\u305f\u3059\u6700\u5c0f\u306e\u6574\u6570 <span class=\"katex-eq\" data-katex-display=\"false\">b\\gt 1000<\/span> \u3092\u6c42\u3081\u3001\u5bfe\u5fdc\u3059\u308b\u5546 <span class=\"katex-eq\" data-katex-display=\"false\">q<\/span> \u3092\u6c7a\u5b9a\u305b\u3088\u3002<\/p>\n<\/li>\n<\/ol>\n<h3>\u7b46\u7b97\u306b\u3088\u308b\u9664\u6cd5\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0<\/h3>\n<p>\u5404\u5834\u5408\u306b\u3064\u3044\u3066\u3001\u7b46\u7b97\u306b\u3088\u308b\u9664\u6cd5\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u3092\u9069\u7528\u3057\u3001\u5546 <span class=\"katex-eq\" data-katex-display=\"false\">q<\/span> \u3068\u4f59\u308a <span class=\"katex-eq\" data-katex-display=\"false\">r<\/span> \u3092\u8a08\u7b97\u305b\u3088\u3002\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306b\u3088\u3063\u3066\u8ca0\u306e\u4f59\u308a\u304c\u5f97\u3089\u308c\u305f\u5834\u5408\u306f\u3001\u7d50\u679c\u3092\u30e6\u30fc\u30af\u30ea\u30c3\u30c9\u9664\u6cd5\u306e\u5f62\u306b\u5909\u63db\u305b\u3088\u3002\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 -37.<\/span><\/span><\/li>\n<\/ol>\n","protected":false},"excerpt":{"rendered":"<p>\u9664\u6cd5\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0 \u672c\u8b1b\u3067\u306f\u3001\u6574\u6570\u306b\u5bfe\u3057\u3066\u4e00\u610f\u306a\u5206\u89e3 \uff08 \u3092\u6e80\u305f\u3059\uff09\u3092\u5f62\u5f0f\u5316\u3059\u308b\u539f\u7406\u3068\u3057\u3066\u3001\u9664\u6cd5\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u3092\u5c55\u958b\u3059\u308b\u3002\u307e\u305a\u5546\u3068\u4f59\u308a\u306e\u5b58\u5728\u3092\u8a3c\u660e\u3057\u3001\u6b21\u306b\u305d\u306e\u4e00\u610f\u6027\u3092\u793a\u3059\u3002\u6700\u5f8c\u306b\u3001\u4f59\u308a\u306e\u610f\u5473\u3092\u89e3\u91c8\u3057\u3001\u7406\u8ad6\u3092\u8a08\u7b97\u624b\u7d9a\u304d\u3068\u3057\u3066\u306e\u7b46\u7b97\u306b\u3088\u308b\u9664\u6cd5\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u3068\u7d50\u3073\u4ed8\u3051\u3001\u3055\u3089\u306b\u5408\u540c\u7b97\u8853\u304a\u3088\u3073\u8a08\u7b97\u6a5f\u5fdc\u7528\u3068\u306e\u81ea\u7136\u306a\u95a2\u9023\u3092\u4e88\u544a\u3059\u308b\u3002 \u5b66\u7fd2\u76ee\u6a19 \u672c\u8b1b\u3092\u4fee\u4e86\u3059\u308b\u3068\u3001\u5b66\u751f\u306f\u6b21\u306e\u3053\u3068\u304c\u3067\u304d\u308b\u3088\u3046\u306b\u306a\u308b\u3002 \u8b58\u5225\u3059\u308b\uff1a\u6574\u6570\u9664\u6cd5\u306b\u304a\u3051\u308b\u57fa\u672c\u7684\u6982\u5ff5\u304a\u3088\u3073\u5f79\u5272\uff08\u88ab\u9664\u6570\u3001\u9664\u6570\u3001\u5546\u3001\u4f59\u308a\uff09\u3068\u3001\u53b3\u5bc6\u306a\u5834\u5408\u3068\u3057\u3066\u306e\u53ef\u9664\u6027\u306e\u6982\u5ff5\u3002 \u8aac\u660e\u3059\u308b\uff1a\u30e6\u30fc\u30af\u30ea\u30c3\u30c9\u9664\u6cd5\u306e\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\uff0f\u5b9a\u7406\u306e\u547d\u984c\u3001\u4f59\u308a\u3092\u898f\u5b9a\u3059\u308b\u6761\u4ef6\uff08\uff09\u304a\u3088\u3073\u66d6\u6627\u3055\u3092\u907f\u3051\u308b\u305f\u3081\u306e\u305d\u306e\u76ee\u7684\u3002 \u9069\u7528\u3059\u308b\uff1a\u5177\u4f53\u4f8b\u306b\u304a\u3044\u3066\u3001\u30e6\u30fc\u30af\u30ea\u30c3\u30c9\u5206\u89e3 \u3092\u7528\u3044\u3066 \u3068 \u3092\u6c7a\u5b9a\u3057\u3001\u4f59\u308a\u306e\u4e0a\u754c\u3092\u78ba\u8a8d\u3059\u308b\u3002 \u5206\u6790\u3059\u308b\uff1a\u88ab\u9664\u6570\u304a\u3088\u3073\u9664\u6570\u306e\u7b26\u53f7\u306b\u5fdc\u3058\u305f\u5834\u5408\u5206\u3051\u306e\u6271\u3044\u3092\u691c\u8a0e\u3057\u3001\u30e6\u30fc\u30af\u30ea\u30c3\u30c9\u306e\u898f\u7d04\u304c\u4f59\u308a\u3092\u975e\u8ca0\u306b\u4fdd\u3064\u7406\u7531\u3092\u6b63\u5f53\u5316\u3059\u308b\u3002 \u5b9f\u884c\u3059\u308b\uff1a\u4f4d\u53d6\u308a\u8868\u73fe\u306b\u57fa\u3065\u304f\u6a5f\u68b0\u7684\u624b\u7d9a\u304d\u3068\u3057\u3066\u306e\u7b46\u7b97\u306b\u3088\u308b\u9664\u6cd5\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u3092\u5b9f\u884c\u3057\u3001 \u3068 \u3092\u5f97\u308b\u3002 \u5185\u5bb9\u7d22\u5f15: \u9664\u6cd5\u3068\u53ef\u9664\u6027 \u30e6\u30fc\u30af\u30ea\u30c3\u30c9\u9664\u6cd5\u306e\u5b9a\u7406 \u30e6\u30fc\u30af\u30ea\u30c3\u30c9\u9664\u6cd5\u306e\u8a3c\u660e \u5546\u3068\u4f59\u308a\u306e\u89e3\u91c8 \u7b46\u7b97\u306b\u3088\u308b\u9664\u6cd5\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0 \u7d50\u8ad6 \u6f14\u7fd2\u554f\u984c\uff08\u4f8b\u984c\u30fb\u89e3\u7b54\u4ed8\u304d\uff09 \u9664\u6cd5\u3068\u53ef\u9664\u6027 \u7b97\u8853\u306b\u304a\u3044\u3066\u3001\u53ef\u9664\u6027\u306f\u300c\u53b3\u5bc6\u306a\u300d\u5834\u5408\u3092\u8868\u3059\u3002\u3059\u306a\u308f\u3061\u3001 \u306f\u3001 \u304c \u306e\u500d\u6570\u3068\u3057\u3066\u6b63\u78ba\u306b\u8868\u3055\u308c\u308b\u3053\u3068\u3092\u610f\u5473\u3059\u308b\u3002\u3057\u304b\u3057\u3001\u4efb\u610f\u306e\u4e8c\u3064\u306e\u6574\u6570\u306e\u9593\u306b\u5e38\u306b\u53ef\u9664\u6027\u304c\u6210\u308a\u7acb\u3064\u308f\u3051\u3067\u306f\u306a\u3044\u3002\u305d\u308c\u3067\u3082\u306a\u304a\u3001\u300c\u3042\u308b\u6570\u304c\u5225\u306e\u6570\u306b\u4f55\u56de\u542b\u307e\u308c\u308b\u304b\u3001\u305d\u3057\u3066\u6b63\u78ba\u306b\u542b\u307e\u308c\u306a\u3044\u5834\u5408\u306b\u4f55\u304c\u6b8b\u308b\u306e\u304b\u300d\u3092\u554f\u3046\u3053\u3068\u306f\u3067\u304d\u308b\u3002\u3053\u306e\u6587\u8108\u306b\u304a\u3044\u3066\u9664\u6cd5\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u304c\u73fe\u308c\u3001\u4efb\u610f\u306e\u6574\u6570 \u304c \u306e\u500d\u6570\u3068\u300c\u4f59\u308a\u300d\u306e\u548c\u3068\u3057\u3066\u8868\u3055\u308c\u308b\u3053\u3068\u3092\u4fdd\u8a3c\u3059\u308b\u3002 \u4f8b\u3068\u3057\u3066\u3001 \u304a\u3088\u3073 \u3092\u8003\u3048\u308b\u30023 \u306f 16 \u3092\u5272\u308a\u5207\u3089\u306a\u3044\u3053\u3068\u306f\u660e\u3089\u304b\u3067\u3042\u308b\u3002\u3057\u304b\u3057\u3001\u9664\u6cd5\u306e\u64cd\u4f5c\u306b\u5bfe\u3057\u3066\u5546\u3068\u4f59\u308a\u3092\u898b\u3064\u3051\u308b\u3053\u3068\u306f\u53ef\u80fd\u3067\u3042\u308a\u3001\u5b9f\u969b \u3057\u305f\u304c\u3063\u3066\u3001 \u3092 \u3067\u5272\u308b\u3068\uff08\u3053\u3053\u3067 \u306f\u88ab\u9664\u6570\u3001 \u306f\u9664\u6570\u3067\u3042\u308b\uff09\u3001 \u307e\u305f\u306f \u3068\u8868\u3055\u308c\u3001\u5546\u3068\u3057\u3066 \u3001\u4f59\u308a\u3068\u3057\u3066 \u304c\u5f97\u3089\u308c\u308b\u3002\u4e00\u822c\u306b\u3001\u9664\u6cd5\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306f\u3001 \u3092\u6e80\u305f\u3059\u4efb\u610f\u306e\u6574\u6570 \uff08\u9664\u6570\uff09\u304a\u3088\u3073 \uff08\u88ab\u9664\u6570\uff09\u306b\u5bfe\u3057\u3066\u3001\u6b21\u3092\u6e80\u305f\u3059\u4e00\u610f\u306a\u6574\u6570 \u3068 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