Divisibility

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

Proposition 1: