Note on the diophantine equation X^t+Y^t=BZ^t

TL;DR

This paper investigates integer solutions to the Diophantine equation X^t + Y^t = BZ^t, providing new results under specific conditions on B and prime t, contributing to the understanding of such equations.

Contribution

It presents novel findings on solutions to the equation for certain rational B and prime t, expanding existing knowledge in number theory.

Findings

Derived new conditions for solutions based on B and t

Identified classes of solutions under specific constraints

Extended previous results in Diophantine equations

Abstract

In this paper, we obtain new results on the integers solutions X, Y, Z of the diophantine equation X^t+Y^t=BZ^t for a rationnal integer B and a prime number t verifying some conditions explained in the paper.