There is a proof on this page: Quadratic Residues
I cannot find a proof/ reasoning behind the following statement:
If p is an odd prime then among the integers in there are exactly quadratic residues and exactly nonresidues.
My text says the reasoning behind this follows from the following fact:
Let be a primitive root modulo and assume . Let be any integer such that . Then is even if and only if is a quadratic residue modulo .
But I don't really see how that follows from this. Any help would be appreciated.
Thanks.
There is a proof on this page: Quadratic Residues