About the Diophantine Equation $x^{4}-q^{4}=py^{r}$

TL;DR

This paper investigates integer solutions to the Diophantine equation x^4 - q^4 = p y^r, extending previous research and providing new theoretical insights into its solutions.

Contribution

The paper proves a new theorem characterizing solutions to the equation, advancing the understanding of this class of Diophantine equations.

Findings

Extended previous results on the equation

Provided new conditions for solutions

Enhanced theoretical framework for Diophantine equations

Abstract

In this paper, we prove a theorem about the integer solutions to the Diophantine equation $x^{4}-q^{4}=py^{r}$, extending previous work of K.Gy\H ory, and F.Luca and A.Togbe, and of the author.