Integer is Congruent Modulo Divisor to Remainder/Corollary

Corollary to Congruence to Remainder
Let $a \equiv b \pmod m$ denote that $a$ and $b$ are congruent modulo $m$.

$a \equiv b \pmod m$ iff $a$ and $b$ have the same remainder when divided by $m$.

Proof
Follows directly from Congruence to Remainder and Congruence (Number Theory) is Equivalence Relation.