The number $n^4 + 4$ is never prime for $n>1$ I am taking a basic algebra course, and one of the proposed problems asks to prove that  $n^4 + 4$ is never a prime number for $n&gt;1$.

I am able to prove it in some particular cases, but I am not able to do it when $n$ is an odd multiple of $5$.
$n^4 + 4 = (2 - 2 n + n^2) (2 + 2 n + n^2)$
More generalized: $a^4 + 4b^4 = a^4 + 4a^2b^2 + 4b^4 - 4a^2b^2 = (a^2 + 2b^2)^2 - (2ab)^2 = (a^2+2b^2-2ab)(a^2+2b^2+2ab)$