I have a problem to solve, which looks like this: $$a^4+4=b$$
$a$ is a natural number where when it is multiplied by the exponent, it'll be equal to $b$
$b$ is always a prime number
We have to find what number is $a$
First off, every time $a$ is multiplied by the exponent and added by 4, it'll always be an even number no matter what. The problem said that the set for the problem will at least have one number, but I couldn't seem to think of a way it can be so. Any help will be appreciated.
Cheers,
For $a>1$ , $b $ cannot be prime because $a^4 + 4 = (a^2 + 2 + 2a)(a^2+2-2a)$
Note: This is a special case of Sophie German identity which gives factors of $a^4 + 4 c^4$