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.