Proof of the conjecture of Keskin, Siar and Karaatli

TL;DR

This paper proves a conjecture related to a specific Diophantine equation involving quadratic and exponential terms, advancing understanding in number theory.

Contribution

It provides a proof of the conjecture of Keskin, Siar, and Karaatli concerning solutions to a particular Diophantine equation.

Findings

Confirmed the conjecture for all cases considered.

Established conditions for solutions to the equation.

Enhanced understanding of the structure of solutions.

Abstract

In this paper among other results, we will prove the conjecture of Keskin, Siar and Karaatli on the Diophantine equation $x^{2}-kxy+y^{2}-2^{n}=0$.