$R$ is a relation defined on the set $\mathbb Z$ of integers.
For any $a,b \in \mathbb Z$, $a\,R\,b$ iff for any prime number $p$,one has $p\,|\,a$ if and only if $p\,|\,b$.
I'm trying to prove or disprove if $R$ is reflexive, symmetric, transitive and anti-symmetric, but I'm having problems understand the question. Is the question saying that all prime numbers must divide a and b for there to be a relation $aRb$ in the first place, or just the existence of one? For instance, do i have a relation $2\, R\, 4$ because $2$ is a prime number that divides both a and b? If so, what's the difference between this question and
For any $a,b \in \mathbb Z$, $a\,R\,b$ iff there exists a prime number $p$ such that $p\,|\,a$ and $p\,|\,b$?