Category archives: Number Theory

Divisibility Divisibility is the true starting point of number theory because it turns the integers into a structured system: numbers are no longer viewed merely as “quantities”, but as elements that either fit together or do not. With a single relation, , it is possible to express everything from simplification...

The Division Algorithm In this class we will develop the division algorithm as the principle that formalizes, for integers, the unique decomposition with . The existence of the quotient and the remainder is first proved, and then their uniqueness. Finally, the meaning of the remainder is interpreted, the theory is...