Let $n \in \mathbb{N}$. Define a relation $\sim_n$ on $\mathbb{Z}$ by
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\begin{align*}
a \sim_n b \quad \text{if and only if} \quad a \equiv b \pmod{n}.
\end{align*}
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Then $\sim_n$ is an [equivalence relation](/page/Equivalence%20Relation) on $\mathbb{Z}$; that is, for all $a,b,c \in \mathbb{Z}$, the relation is reflexive, symmetric, and transitive.