Let be two quadratic residues of the prime that satisfy . Prove that (mod ) is impossible.
The hint says to use the theorem " if and only if no prime in the factorization of occurs to an odd power.
Suppose (mod ). Since are two quadratic residues of the , (mod ) and (mod ). So (mod ). So for some .
I also know that , so .
I think I should end up contracting the theorem above, but I'm kinda stuck.. can I get some help please?