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