Well we always have . So in this case, by assumption we have . You are asked to show that, although , is not a square modulo .
The point of the exercise is to realize that implies that is not a square, but that does not imply that is a square.
The problem is
"Suppose n=pq where pq are distinct odd primes. prove that there always exist positive integers a,b, such that
and , and such that is not a square modulo n."
Does for ab to not be a square modulo n mean ?
I think I'm doing it wrong because I keep getting .
Could anyone give me a hand with this?