Congruence class
= Congruence class
{title2=$[a]_N$}
The <congruence class> of $a$ modulo a positive integer $N$ is $\{a+Nk:k\in\mathbb Z\}$. Two integers have the same class exactly when their difference is divisible by $N$. Addition and multiplication of representatives descend to well-defined operations on $\mathbb Z/N\mathbb Z$, because replacing a representative by a multiple-of-$N$ translate changes the result by a multiple of $N$.