Galois groups of Fermat polynomials and the arithmetic groups of Diophantine curves

TL;DR

This paper introduces an algebraic framework using Newtonian triangles to analyze Diophantine equations, applying it to Fermat's Last Theorem and exploring its implications.

Contribution

It presents a novel algebraic approach with Newtonian triangles to study Diophantine equations and their relation to Fermat's Last Theorem.

Findings

Framework simplifies analysis of Diophantine equations.

Provides new insights into Fermat's Last Theorem.

Discusses consequences for number theory.

Abstract

This paper develops a framework of algebra whereby every Diophantine equation is made quickly accessible by a study of the corresponding row entries in an array of numbers which we call the Newtonian triangles. We then apply this framework to the understandimg of the Fermat's Last Theorem and discuss some of its direct consequences.