Definition:Congruence (Number Theory)/Residue

From ProofWiki
Jump to navigation Jump to search

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 $\mathsf{Pr} \infty \mathsf{fWiki}$ is designated as the least positive residue.


Also see


Sources