How can I show that $S$ is an equivalence relation:
Given a relation $S$ on $\mathbb N$ such that:
$$ (n,m) \in S \text{ if } m^2 \text{ is divisible by } n $$
I know equivalence relations are symmetric, reflexive and transitive. I'm just not sure how to use this knowledge to prove it.
Reflexive:
I believe I need to show that for any $x \in \mathbb N$, $(x\,,\,x) \in
S$.
I'm unsure how I prove this for reflexive, symmetric, and transitive.
$\in$
for $\in$. $\endgroup$