\begin{definition}[Definition:Congruence (Number Theory)/Integers/Modulo Operation]
Let $m \in \Z_{>0}$.
Let $\bmod$ be defined as the modulo operation:
:$x \bmod m := \begin{cases}
x - m \left \lfloor {\dfrac x m}\right \rfloor & : m \ne 0 \\
x & : m = 0
\end{cases}$
Then '''congruence modulo $m$''' is the relation on $\Z$ defined as:
:$\forall x, y \in \Z: x \equiv y \pmod m \iff x \bmod m = y \bmod m$ 
The integer $m$ is called the '''modulus'''.
\end{definition}