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