\begin{definition}[Definition:Congruence (Number Theory)/Integers/Integer Multiple]
Let $m \in \Z_{> 0}$ be an integer.
Let $x, y \in \Z$.
'''$x$ is congruent to $y$ modulo $m$''' {{iff}} their difference is an integer multiple of $m$:
:$x \equiv y \pmod m \iff \exists k \in \Z: x - y = k m$
\end{definition}