On a diophantine equation of M. J. Karama

TL;DR

This paper constructs infinite families of positive integer solutions for the diophantine equation x^n - y^n = z^{n+1} for all positive integers n, expanding understanding of its solution space.

Contribution

It introduces a method to generate infinite solutions for the equation x^n - y^n = z^{n+1} for all positive n, which was previously unexplored.

Findings

Infinite solutions exist for all positive n

A constructive method to find solutions is provided

The solutions form an infinite family

Abstract

For every positive integer $n$, an infinite family of positive integral solutions of the diophantine equation $x^n - y^n = z^{n+1}$ is constructed.