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 $n>1$.
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 $5$.   

Hint $\ $ Completing the square leads to a difference of squares
$$\begin{eqnarray} &&\ \, n^4 + 2^2\\ \,&=&\, (n^2\!+2)^2\!-(2n)^2\\ \,&=&\, (n^2\!+2\ -\ 2n)\ (n^2\!+2\ +\ 2n)\end{eqnarray}$$
