Modulo operation ($a\mathrm{mod}m$)

For an integer $a$ and a positive integer modulus $m$, the modulo operation returns the unique least nonnegative residue $r$ satisfying $a=qm+r$ for an integer $q$ and $0\le r<m$. Equivalently, $r=a-m\lfloor a/m\rfloor$. For example, $-3\mathrm{mod}5=2$. Some programming languages instead use a remainder with the sign of the dividend, so their negative-input convention must be checked before identifying an operator with this mathematical definition.