Let p be an odd prime and let g be a primitive root modulo p (i. e., F ∗ p = {1, g, g2 , . . . , gp−2}), and let a be an integer. (a) Prove that if the discrete logarithm log (a) is even, then a has a square root modulo p. (I. e., there exists an integer b such that b 2 ≡ a (mod p).)