The Mordell-Schinzel conjecture for cubic diophantine equations

TL;DR

This paper proves that certain cubic Diophantine equations, specifically those of the form xyz=G(x,y), have infinitely many solutions, extending previous foundational work by Mordell and Schinzel.

Contribution

It establishes the infinitude of solutions for a class of cubic Diophantine equations, advancing the understanding of their solution sets.

Findings

Proved that xyz=G(x,y) has infinitely many solutions.

Extended Mordell's and Schinzel's previous results.

Contributed to the theory of cubic Diophantine equations.

Abstract

Building on the works of Mordell (1952) and Schinzel (2015), we prove that cubic diophantine equations $xyz=G(x,y)$ have infinitely many solutions.