 Least nonnegative residue

The least nonnegative residue of an integer $a$ modulo a positive integer modulus $m$ is the unique representative $r$ of its congruence class in $\{0,\dots ,m-1\}$. Euclidean division gives $a=qm+r$. For example, $-3=(-1)\cdot 5+2$, so $-3\mathrm{mod}5=2$; the integer congruence $-3\equiv 2(\mathrm{mod}5)$ does not assert equality of those two integers.