Definition:Congruence (Number Theory)/Residue

Definition
Let $m \in \Z_{\ne 0}$ be a non-zero integer. Let $a, b \in \Z$.

Let $a \equiv b \pmod m$.

Then $b$ is a residue of $a$ modulo $m$.

Residue is another word meaning remainder, and is any integer congruent to $a$ modulo $m$.

Also defined as
Some sources define the residue to be the smallest (non-negative) integer congruent to $a$ modulo $z$, that is, what on is designated as the least positive residue.

Also see

 * Definition:Least Positive Residue


 * Definition:Complete Residue System