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Definition (Modular Equivalence, Congruent Mod $n$)
Let $n$ be a natural number, and let $a,b\in \mathbb{Z}$. We say that $a$ is congruent to $b$ mod $n$ and write $a\cong b \pmod{n}$ if and only if $a$ and $b$ have the same remainder upon division by $n$. Since we know two integers have the same remainder upon division by $n$ if and only if $n$ divides their difference, we can say that $$a\cong b \pmod{n}\ \quad \text{if and only if}\quad n \text{ divides } a-b.$$