define $a \equiv b\ \ \ (mod\ n)$
read "$a$ is congruent to $b$, mod $n$"

$\exists(a \in \mathbb{Z}) \land \exists(b \in \mathbb{Z}) \land \exists(n \in \mathbb{Z}) \land$

$(a \equiv b\ \ \ \ mod(n)) \Longleftrightarrow (n|a-b)$

Suppose $a, b$ and $n$ are integers. we can declare that $a$ is congruent to $b$ mod $n$ if and only if $n$ divides $a$ minus $b$.

(10)

define $a \equiv b\ \ \ (mod\ n)$read "$a$ is congruent to $b$, mod $n$"