Integer is Congruent Modulo Divisor to Remainder/Corollary

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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.

$\blacksquare$