Hi I am supposed to prove that R is an equivalence relation on N (natural number)
We define the relation R on N as aRb if $ab=k^2$ for some k that belongs to N.
I know that I should prove that the relation is reflexive, symmetric and transitive.
The relation is reflexive if aRa for some a that belongs to N. a^2 is a natural number and therefore a^2 = k^2 and aRa.
The relation is symmetric if aRb then bRa for all a and b that belongs to N.
The relation is symmetric because if aRb then $ab=k^2$ for some k that belongs to Z. This is equivalent to $ba= k^2$ and therefore bRa.
I'm not sure about Transitive tho. I must prove that if aRb and bRc then aRc. How can I do that?