I got the following problem.
Prove that $p=a^4+4b^4 \;\;\;$can not be a prime number, $\;\; p\gt 5$
I know that $p=(a^2)^2+(2b^2)^2$ can be written as the sum of two squares if and only if $\;\;p\equiv 1 \mod \;4$.
Hence $a \equiv 1$ or $a\equiv 3 \mod \;4$
I dont know how can I continue from here