Congruent to Zero iff Modulo is Divisor

Theorem
Let $$a \in \mathbb{Z}, m \in \mathbb{N}$$.

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

$$m \backslash a \iff a \equiv 0 \left({\bmod\, m}\right)$$

Proof
Thus by definition of congruence modulo m, $$a \equiv 0 \left({\bmod\, m}\right)$$ and the result is proved.