Definition:Set of Residue Classes/Least Positive

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 $$a \equiv r \left({\bmod\, m}\right)$$ from Congruence to an Integer less than Modulus.

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

Some sources call this the common residue.

Compare with

 * Least Absolute Residue