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Old 2012-10-31, 14:16   #7
science_man_88
 
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Jul 2009
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Quote:
Originally Posted by Unregistered View Post
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.
well assume gcd(a,b)=c then the equation comes to:

(a^n+b^n)/(a+b) = c^n*(d^n+e^n)/c*(d+e) =c^(n-1)*(d^n+e^n)/(d+e) so if (d^n+e^n)/(d+e) is integer so is (a^n+b^n)/(a+b) but with a integer divisor >1 so it's not prime.
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