\begin{definition}[Definition:Integer Division]
Let $a, b \in \Z$ be integers such that $b \ne 0$..
From the Division Theorem:
:$\exists_1 q, r \in \Z: a = q b + r, 0 \le r < \left|{b}\right|$
where $q$ is the quotient and $r$ is the remainder.
The process of finding $q$ and $r$ is known as '''(integer) division'''.
\end{definition}