Definition:Set of Residue Classes/Least Positive

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 Congruence to an 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.

Also see

 * Definition:Least Absolute Residue