# Definition:Reduced Residue System/Least Positive Residue

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## Definition

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

Let $r$ be the smallest non-negative integer in $\left[\!\left[{a}\right]\!\right]_m$.

$0 \le r < m$

and:

$a \equiv r \pmod m$

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

## Also known as

Some sources call this the common residue.