Definition:Integer Division

Definition
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.