Thanks so much for your replies. Very helpful.
Batalov, if I understand your arguments, if n is odd and composite then (a^n+b^n)/(a+b) must also be composite. Can this be extended to any composite n with an odd factor? If so, then only n that are powers of two could possibly result in a prime. I have found some counterexamples and have observed that a and b are never coprime. Can you think of an argument to support this observation about coprimes? Thanks.
