prime numbers and natural numbers

Question

Prove that $n^4+4^n$ is never prime. Here $n$ is any natural number greater than $1$. I have tried by induction hypothesis but to no avail. Can it be done by considering cases when $n$ is odd and when it is even?

Answer 1

(1) If $n$ is odd, $n^4+4^n=(n^2+2^n-2^{n+1\over2}n)(n^2+2^n+2^{n+1\over2}n)$.

(2) If $n$ is even then $4|n^4+4^n$.

Answer 2

on binomial expansion of (2k+1)^2,all terms are multiples of 4 but one term is 1.so 4 cannot be taken common.