State Euclid's division lemma.

Question:

State Euclid's division lemma.

Solution:

Euclid’s Division Lemma:

Let and b be any two positive integers.

Then, there exist unique integers q and r such that 

$a=b q+r, 0 \leq r

If $b \mid a$ then $r=0$.

Otherwise, $r$ satisfies the stronger inequality $0

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