Competition problem — Number theory

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Number theory Difficulty 6.3 National olympiad Prove it

The Division Theorem
Algorithm $\qquad$ If $a$ and $b$ are integers such that $b>0$ , then there are unique integers $q$ and $r$ such that $a=b q+r$ with $0 \leqslant r<b$ .

In the equation given in the division algorithm, we call $q$ the quotient and $r$ the remainder.

Solution

None

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Source: NuminaMath-1.5, licensed Apache-2.0. Statement and solution reproduced as published; topic and difficulty added by this site.