How many ordered triple $ (p,a,b) $ is possible such that $p^a=b^4+4$? If we have a prime number $p$ and two natural numbers $a$ and $b$ such that $p^a=b^4+4$,
then how many such ordered triplets $(p,a,b)$ exist?
What should be the strategy to solve this one? The only I can see is $(5,1,1)$, is this the only one? if yes, how could we prove that?

It depends on your definition of natural number, but $(2,2,0)$ may be the only other possibility
