I'm currently studying for an exam and I've come across this question:
Define a relation R on Z by
xRy ⇔ 6|($x^{2} − y^{2}$)
for x, y ∈ Z.
Prove that R is an equivalence relation and describe the equivalence classes of R
I understand how to prove it's reflexive, and I've tried to prove it's symmetric but I used the fact that -6|($y^{2}-x^{2}$) which doesn't seem like the correct way to answer this question, and I have no idea how to prove it's transitive, any help would be greatly appreciated. Thanks in advance!