Definition:Modulo Addition/Definition 2

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

$\forall a, b \in \Z_m: a +_m b$ equals the remainder after $a + b$ has been divided by $m$


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


Sources