(2) Let p be an odd prime. Let A be the sum of all quadratic residues...

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(2) Let p be an odd prime. Let A be the sum of all quadratic residues 1 < a<p and B be the sum of all non-residues 1<a< p. (1) Show that if p = 3 (mod 4) then A = B (mod p). (2) Show that if p 1 (mod 4) then A B (mod p). (2) Let p be an odd prime. Let A be the sum of all quadratic residues 1 < a<p and B be the sum of all non-residues 1<a< p. (1) Show that if p = 3 (mod 4) then A = B (mod p). (2) Show that if p 1 (mod 4) then A B (mod p).