Difference radical in terms of shifting zero and applications to the Stothers-Mason theorem

TL;DR

This paper explores the concept of shifting zeros and an analogue to the difference radical, applying these ideas to the Stothers-Mason theorem and difference Fermat-type equations, with illustrative examples.

Contribution

It introduces a difference radical concept related to shifting zeros and applies it to extend the Stothers-Mason theorem and Fermat-type equations.

Findings

New difference radical concept introduced

Extended Stothers-Mason theorem using falling factorials

Provided examples of difference Fermat equations

Abstract

In this paper, we study the shifting zeros with its heights and an analogue to difference radical. We focus on the Stothers-Mason theorem by using falling factorials. As applications, we discuss the difference version of the Fermat type functional equations. Some examples are given.