Definition:Modulo Addition/Definition 1

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

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

$\Z_m = \set {\eqclass 0 m, \eqclass 1 m, \ldots, \eqclass {m - 1} m}$

where $\eqclass x m$ is the residue class of $x$ modulo $m$.

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

$\eqclass a m +_m \eqclass b m = \eqclass {a + b} m$

Also denoted as

Although the operation of addition modulo $m$ is denoted by the symbol $+_m$, if there is no danger of confusion, the conventional addition symbol $+$ etc. is often used instead.

The notation for addition of two residue classes modulo $m$ is not usually $\eqclass a m +_m \eqclass b m$.

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

Also see