On the solutions of $x^p+y^p=2^r{z}^p$, $x^p+y^p=z^2$ over totally real fields

Narasimha Kumar, Satyabrat Sahoo

In this article, we study the non-trivial primitive solutions of a certain type for the Diophantine equations $x^p+y^p=2^r{z}^p$ and $x^p+y^p=z^2$ of prime exponent $p$, $r \in \math…