# Integer is Congruent Modulo Divisor to Remainder/Corollary

## Corollary to Integer is Congruent Modulo Divisor to Remainder

Let $a \equiv b \pmod m$ denote that $a$ and $b$ are congruent modulo $m$.

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

## Proof

Follows directly from:

Integer is Congruent Modulo Divisor to Remainder
Congruence Modulo Real Number is Equivalence Relation.

$\blacksquare$