congruent modulo

• Given integers $a$ and $b$ and $n\in \mathbb{N}$, we say that $a$ and $b$ are congruent modulo $n$ if $n|(a-b)$. We express this as $a\equiv b$ (mod n). If $a$ and $b$ are not congruent modulo $n$, we write this as $a\not\equiv b$ (mod n).