An Exponential Diophantine Equation - One Order Higher than Fermat's Equation

TL;DR

This paper introduces a new exponential Diophantine equation that extends Fermat's Last Theorem, providing examples of solutions and proposing a related conjecture.

Contribution

It formulates a higher-order exponential Diophantine equation, offers explicit solutions, and presents a conjecture, advancing the understanding of exponential Diophantine problems.

Findings

Three explicit solutions to the new equation

Formulation of a related conjecture

Extension of Fermat's Last Theorem concept

Abstract

We formulate an exponential Diophantine equation, which is is some sense one order higher that Fermat's Last Theorem. We also give three examples of solutions to this exponential Diophantine equation and formulate a conjecture.