Thread: bout the quadratic reciprocity law

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.

Originally Posted by felixmcgrady

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).

I do this one and #2 and #3 should be similar. If is primitive root then are the quadradic residues i.e. the even exponents of . Their product is . Notice that .
Thus, their product is congruent to .