# Definition:Reduced Residue System/Least Positive Residue

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< 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 $m$).

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

Then from Integer is Congruent to Integer less than Modulus:

- $0 \le r < m$

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**.