Let p be an odd prime number. Prove the following facts about squares modulo p. Use primitive roots to prove a) to d)

(a) The number of quadratic residues modulo p is the same as the number of nonquadratic residues.

(b) The product of two quadratic residues is again a quadratic residue.

(c) The product of two nonquadratic residues is a quadratic residue.

(d) The product of a quadratic residue and nonquadratic residue is a nonquadratic residue.

(e) Use the previous facts to justify that the Legendre Symbol satisfies (ab/p) = (a/p) (b/p) for any integers a, b.