I'm having a bit of trouble in proving the equivalence classes of the relation. I've already written proof that the relation is an equivalence relation. I'm hoping for someone to give me some insights on the question below.
Consider the relation $R$ on $\mathbb{Z}$ given by $R$ = {($a, b$) ∈ $\mathbb{Z}$ × $\mathbb{Z}$ : $4$ | ($a^2 - b^2$)}.
Describe the distinct equivalence classes of $R$ and prove that they are the equivalence classes.