Equality of Squares Modulo Integer is Equivalence Relation

Theorem
Let $n \in \Z_{>0}$ be a (strictly) positive integer.

Let $\mathcal R_n$ be the relation on the set of integers $\Z$ defined as:
 * $\forall x, y \in \Z: x \mathrel {\mathcal R_n} y \iff x^2 \equiv y^2 \pmod n$

Then $\mathcal R_n$ is an equivalence relation.