Let p be a prime such that p = 2²″ + 1, for some n € N, with n > 1. Let p (a) Determine if 5 is a quadratic residue or a quadratic nonresidue modulo p. (b) Use the result of (a) to prove that 5 is a primitive root modulo p. (c) Use the result of (b) to determine a complete set of representatives for all the solutions modulo 257 of x6 = 25(mod 257).