\begin{definition}[Definition:Modulo Addition/Definition 2]
Let $m \in \Z$ be an integer.
Let $\Z_m$ be the set of integers modulo $m$:
:$\Z_m = \set {0, 1, \ldots, m - 1}$
The operation of '''addition modulo $m$''' is defined on $\Z_m$ as:
:$\forall a, b \in \Z_m: a +_m b$ equals the remainder after $a + b$ has been divided by $m$
\end{definition}