Congruent to Zero iff Modulo is Divisor

Theorem
Let $$a \in \Z, m \in \N$$.

Then $$a$$ is congruent to $$0$$ modulo $$m$$ iff $$m$$ is a divisor of $$a$$.


 * $$m \backslash a \iff a \equiv 0 \pmod m$$

Proof
$$ $$ $$

Thus by definition of congruence modulo m, $$a \equiv 0 \pmod m$$ and the result is proved.