Let $x$ be an integer and $n$ be a positive integer. Find the smallest $n$ such that $x^4+n^2$ is not a prime for any $x$. I need help proving the following: Let $x$ be an integer and $n$ be a positive integer. Find the smallest $n$ such that $x^4+n^2$ is not a prime for any $x$. I know that the smallest $n$ is 8 by testing $n=1,2,3,...$. I need help proving that $n=8$ is the smallest $n$ such that $x^4+n^2$ is not a prime for any $x$. 

Hint:
$$ x^4+4m^4 = (x^4+4x^2m^2+4m^4)-(4x^2m^2)=(x^2+2m^2)^2-(2mx)^2 = (x^2-2mx+2m^2)(x^2+2mx+2m^2).$$
