Definition:Multiplication/Modulo Multiplication/Definition 2

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Let $m \in \Z$ be an integer.

Let $\Z_m$ be the set of integers modulo $m$:

$\Z_m = \left\{{0, 1, \ldots, m-1}\right\}$

The operation of multiplication modulo $m$ is defined on $\Z_m$ as:

$x \cdot_m y$ equals the remainder after $x y$ 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.

Also see

  • Results about modulo multiplication can be found here.