(a) Prove that if p and q are odd primes and q | aP - 1, then either q|a q=2kp+1 for some integer k. or else [Hint: Because aP = 1 (mod q), the order of a modulo q is either 1 or p; in the latter case, po(q).] b) Use part (a) to show that if p is an odd prime, then the prime divisors of 2P - 1 are of the form 2kp + 1. C) Find the smallest prime divisors of the integers 217 - 1 and 229 - 1.