If 1+2^n+4^n is prime then prove that n is 3^k.Both variables are natural numbers.

Help would be appreciated.

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- Oct 8th 2013, 07:27 AMRuyHayabusaPrime number
If 1+2^n+4^n is prime then prove that n is 3^k.Both variables are natural numbers.

Help would be appreciated. - Oct 8th 2013, 09:19 AMSlipEternalRe: Prime number
What have you tried so far? My gut is telling me to use the division algorithm . Then since the order of 2 in the multiplicative group of is known to be , you can further use the division algorithm on for some . Maybe an induction argument will arise that will yield that if then 3 divides .