I'm completely lost in discrete mathematics. I have to find out whether $$xRy \iff \exists z\in \mathbb N \;\;[z\mid y \iff z\mid x]$$ where $x,y \in \mathbb N$ is an equivalence.
I know that relation must be reflexive, symmetric and transitive in order to be an equivalence.
If relation is reflexive, then $z\mid x \iff z\mid x$ must be the same, which is true. But I have no idea how to prove symmetry and transitivity of relation. Thanks for your advice