Question 4

A) Use theorem 3.14 and 3.16 to find all primes p for which -2 is a quadratic residue

B) Use Gauss's Lemma to find all primes p for which -2 is a quadratic residue

C) Let P be an odd prime.prove that {2,4,6,...p-1} is a Gaussian set modulo p

D) prove that S= {3,4,5,9,10} is a Goussian set modulo 11. ApplyGauss's Lemma to this set to compute the legendre symbols (3/11) and (7/11)