# Definition:Reduced Residue System/Least Positive Residue

From ProofWiki

< Definition:Reduced Residue System(Redirected from Definition:Least Positive Residue)

## Definition

Let $\left[\!\left[{a}\right]\!\right]_m$ be the residue class of $a$ (modulo $m$).

If $r$ is the smallest non-negative integer in $\left[\!\left[{a}\right]\!\right]_m$, then $0 \le r < m$ and $a \equiv r \pmod m$ from Congruence to an Integer less than Modulus.

Then $r$ is called the **least positive residue** of $a$ (modulo $m$).

## Also known as

Some sources call this the **common residue**.