\begin{definition}[Definition:Congruence (Number Theory)/Notation]
The relation '''$x$ is congruent to $y$ modulo $z$''', usually denoted:
:$x \equiv y \pmod z$
is also frequently seen denoted as:
:$x \equiv y \ \paren {\mathop {\operatorname{modulo} } z}$
Some (usually older) sources render it as:
:$x \equiv y \ \paren {\mathop {\operatorname{mod.} } z}$
Category:Definitions/Modulo Arithmetic
\end{definition}