# Definition:Modulo Multiplication/Definition 2

## Definition

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 $m$.

## Also denoted as

Although the operation of multiplication modulo $m$ is denoted by the symbol $\times_m$, if there is no danger of confusion, the conventional multiplication symbols $\times, \cdot$ etc. are often used instead.

The notation for multiplication of two integers modulo $m$ is not usually $\eqclass a m \times_m \eqclass b m$.

What is more normally seen is $a b \pmod m$.

## Also see

• Results about modulo multiplication can be found here.