I'm looking for information on this kind of reverse-Fermat problem: Given $a,b,c \in \mathbb{C}$, find a $z \in \mathbb{C}$ such that $a^z + b^z = c^z$?
When does such a $z$ exist? Is anything known? Thanks.
I'm looking for information on this kind of reverse-Fermat problem: Given $a,b,c \in \mathbb{C}$, find a $z \in \mathbb{C}$ such that $a^z + b^z = c^z$?
When does such a $z$ exist? Is anything known? Thanks.