(a) Prove that if p and q are odd primes and q I aP - 1, then either q I a - 1 or elseq
Chapter 8, Problem 8(choose chapter or problem)
(a) Prove that if p and q are odd primes and q I aP - 1, then either q I a - 1 or elseq = 2kp + 1 for some integer k.[Hint: Because aP = 1 (mod q), the order of a modulo q is either 1 or p; in the lattercase, p I (q).](b) Use part (a) to show that if p is an odd prime, then the prime divisors of 2P - 1 areof the form 2kp + 1.( c) Find the smallest prime divisors of the integers 217 - 1 and 229 - 1.
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