How can I show that the number of quadratic residues modulo m is equal to the number of quadratic nonresidues modulo m in the set of reduced residue system modulo m?
Note that , , ...
So that the only distinct quadratic residues are: , but we have hence the rest of them must be non-quadratic residues, that is we have quadratic residues and non-quadratic residues.
EDIT: Thought I'd clarify a bit: if and only if since p is prime either or