\begin{definition}[Definition:Coprime Residue Class]
Let $m \in \Z: m \ge 1$.
Let $a \in \Z$ such that:
:$a \perp m$
where $\perp$ denotes that $a$ is prime to $m$.
Let $\eqclass a m$ be the residue class of $a$ (modulo $m$):
:$\set {x \in \Z: \exists k \in \Z: x = a + k m}$
Then $\eqclass a m$ is referred to as a '''coprime residue class'''.
\end{definition}