Chapter 4.4, Problem 60E

Show that if p is and odd prime, then there are exactly $\left(p-\text{1}\right)/\text{2}$ quadratic residues of p among the integers $\text{1},\text{2},\dots ,p-\text{1}$ .

If p is and odd prime and a is an integer not divisible by p, the Legendre symbol $\left(\frac{a}{p}\right)$ is defined to be 1 if a is a quadratic residue of p and -1 otherwise.