\begin{definition}[Definition:Modulo Multiplication/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 '''multiplication modulo $m$''' is defined on $\Z_m$ as:
:$a \times_m b$ equals the remainder after $a b$ has been divided by $m$.
\end{definition}