I need help with a problem from my discrete math course. I'm sure this problem is rather simple but I just can't figure out how to start it. I know I need to prove it is reflexive, symmetric, and transitive but I don't have any similar examples.
Let $\operatorname R$ be a relation on $\mathbb Z \times\mathbb Z$ such that $(a,b)\operatorname R(c,d) \iff a+b^3=c+d^3$.
Prove that $\operatorname R$ is an equivalence relation.