\begin{definition}[Definition:Modulo Addition/Definition 3]
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:
:$a +_m b := a + b - k m$
where $j$ is the largest integer such that $k m \le a + b$.
\end{definition}