Category:Definitions/Modulo Division

This category contains definitions related to Modulo Division.
Related results can be found in Category:Modulo Division.

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 division modulo $m$ is defined on $\Z_m$ as:

$a \div_m b$ equals the integer $q \in \Z_m$ such that $b \times_m q \equiv a \pmod m$

and is possible only if $q$ is unique modulo $m$.

This happens if and only if $a$ and $m$ are coprime.