A lower bound limiting solutions in the hyperbolic case of the generalized Fermat equation

TL;DR

This paper establishes a lower bound for the sum of reciprocals of exponents in the hyperbolic case of the generalized Fermat equation, constraining possible solutions.

Contribution

It introduces a new lower bound for the sum of reciprocals of exponents in the hyperbolic case of the generalized Fermat equation.

Findings

Derived a specific lower bound for  in the hyperbolic case

Limits the range of exponents for solutions to the equation

Provides a theoretical constraint on solutions in this case

Abstract

We find a lower bound for $\chi = 1/p+1/q+1/r$ limiting any solution in the hyperbolic case of the Generalized Fermat Equation $x^p + y^q = z^r$.