Definition:Modulo Addition/Definition 3

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:
 * $x +_m y := x + y - j m$

where $j$ is the largest integer such that $j m \le x + y$.

Also see

 * Equivalence of Definitions of Integer Modulo Addition