\begin{definition}[Definition:Congruence (Number Theory)/Residue]
Let $m \in \Z_{\ne 0}$ be a non-zero integer.
Let $a, b \in \Z$.
Let $a \equiv b \pmod m$.
Then $b$ is a '''residue of $a$ modulo $m$'''.
'''Residue''' is another word meaning remainder, and is ''any'' integer congruent to $a$ modulo $m$.
\end{definition}