Proof for a relation

Question

Define a relationship $R$ on $\mathbb{Z}$ by declaring that $xRy$ if and only if $x^2 \equiv y^2 (mod 4)$. Prove that $R$ is reflexive, symmetric and transitive.

I'm unsure of where to start with this question.

Answer 1

Not to hard to prove that:

1. $x^2\equiv x^2($mod $4)$ (reflexivity)
2. $x^2\equiv y^2($mod $4)\Rightarrow y^2\equiv x^2($mod $4)$ (symmetric)
3. And $x^2\equiv y^2($mod $4)\wedge y^2\equiv z^2($mod $4)\Rightarrow x^2\equiv z^2($mod $4)$ (transitiv)