Algebra and Number Theory/Elementary Number Theory

Divisibility

Definition 1: Let $a,b\in \mathbb {Z}$$a,b\in \mathbb {Z}$. We say that "$a$$a$ divides $b$$b$" or that "$b$$b$ is a multiple of $a$$a$", if there exists some $q\in \mathbb {Z}$$q\in \mathbb {Z}$ such that $b=aq$$b=aq$.
We write this as $a\mid b$$a\mid b$.

Proposition 1: