Generalized fruit Diophantine equation and super elliptic curves

TL;DR

This paper investigates rational points on superelliptic curves, generalizing fruit Diophantine equations, and explores their properties and solutions.

Contribution

It introduces a generalized framework for fruit Diophantine equations and studies superelliptic curves within this context.

Findings

Characterization of rational points on superelliptic curves

Conditions for solvability of generalized fruit Diophantine equations

New methods for analyzing superelliptic curves

Abstract

In this article, we are interested in finding rational points on certain superelliptic curves.