I hate doing this, but I'm having a lot of trouble figuring this one out. I don't think Mathematical Induction will work but here is the problem anyways:
Show that if a is a positive integer and a^m + 1 is an odd prime, then m = 2^n for some positive integer n. (Hint: Recall the identity a^m + 1 = (a^k + 1)(a^(k*(l-1)) - a^(k(l-2)) + ... - a^k + 1), where m = kl and l is odd).
Basically show all primes in the form a^m + 1 are Fermat Numbers.
Show that if a is a positive integer and a^m + 1 is an odd prime, then m = 2^n for some positive integer n. (Hint: Recall the identity a^m + 1 = (a^k + 1)(a^(k*(l-1)) - a^(k(l-2)) + ... - a^k + 1), where m = kl and l is odd).
Basically show all primes in the form a^m + 1 are Fermat Numbers.
