Prime no.s

https://brilliant.org/problems/it-may-works-for-odd-numbers/?ref_id=1347822

Answer: 0

$n^{4} +4^{n}$ can't be a Prime number.

We will discuss two cases:-

1. $x$ is even $\implies x^4 + 4^x = even.$

2. x is odd

   if $x$ is odd then we can write $x \ \text{as} \ 2n+1$ ; and the given equation can be written as

$(2n +1)^4 + 4^{(2n+1)} = (2n +1)^4 + 4.(2^n)^4$

Which is not a prime.