Hey can any body help me with these?
1. if r is a primitive root of the odd prime p, prove that the product of the quadratic residues of p is congruent modulo p to r^((p^2-1)/4) and the product of the nonresidues of p is congruent modulo p to r^((p^2-1)/4).
2. if the prime p>3, show that p divides the sum of its quadratic residues.
3. if the prime p>5, show that p divides the sum of the squares of its quadratic nonresidues.
Thanks very much, i just dont get these at all.