How many primes are there of the form $a^{k/2} + b^{k/2}$ exist for $a$ and $b$ (positive integer solutions).
I am hoping there is only one.
EDIT $k > 1$
How many primes are there of the form $a^{k/2} + b^{k/2}$ exist for $a$ and $b$ (positive integer solutions).
I am hoping there is only one.
EDIT $k > 1$
Infinitely many. In fact, every prime $p \equiv 1 \pmod 4$ can be written as the sum of two squares; a result attributed to Fermat. And there are infinitely many such primes, according to Dirichlet's Theorem.