On the Solutions of the Diophantine Equation $x^n+y^n=z^n$ In the Finite Fields ${\mathbb{Z}}_p$

Silvia R. Valdes, Yelena Shvets

Let $p$ be a prime integer, ${\mathbb{Z}}_p$ the finite field of order $p$ and ${\mathbb{Z}}_p^{\ast }$ is its multiplicative cyclic group. We consider the Diophantine equation $x^n + y^…