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

Abstract

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

12 pages, Preliminary version