Definition:Set of Residue Classes/Least Absolute

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

Except when $$r = \frac m 2$$, we can choose $$r$$ to the integer in $$\left[\!\left[{a}\right]\!\right]_m$$ which has the smallest absolute value.

In that exceptional case we have $$-\frac m 2 + m = \frac m 2$$ and so $$-\frac m 2 \equiv \frac m 2 \pmod m$$.

So we define $$r$$ as the least absolute residue of $$a$$ (modulo $$m$$) if:
 * $$-\frac m 2 < r \le \frac m 2$$

Compare with

 * Least Positive Residue