An All-Inclusive Proof of Beal’s Conjecture

Stephen M Marshall

doi:10.18052/www.scipress.com/bsmass.7.17

Abstract

This paper presents a complete and exhaustive proof of the Beal Conjecture. The approach to this proof uses the Fundamental Theorem of Arithmetic as the basis for the proof of the Beal Conjecture. The Fundamental Theorem of Arithmetic states that every number greater than 1 is either prime itself or is unique product of prime numbers. The prime factorization of every number greater than 1 is used throughout every section of the proof of the Beal Conjecture. Without the Fundamental Theorem of Arithmetic, this approach to proving the Beal Conjecture would not be possible.

Highlights

D In 1997 an amateur mathematician and Texas banker named Andrew Beal discovered the BealConjecture
The Beal Conjecture states that the only solutions to the equation Ax + By = Cz, when A, B, C, are positive integers, and x, y, and z are positive integers greater than 2, are those in
Last Theorem, which states that there are no solutions to the equation an + bn = cn where a, b, and c are positive integers and n is a positive integer greater than 2

Summary

Introduction

D In 1997 an amateur mathematician and Texas banker named Andrew Beal discovered the Beal. The Beal Conjecture states that the only solutions to the equation Ax + By = Cz, when A, B, C, are positive integers, and x, y, and z are positive integers greater than 2, are those in. The truth of the Beal Conjecture implies Fermat's. Last Theorem, which states that there are no solutions to the equation an + bn = cn where a, b, and c are positive integers and n is a positive integer greater than 2. The theorem was proved in the 1990s by Andrew Wiles, together with Richard Taylor. Both the Beal Conjecture and Fermat's Last Theorem are typical of many statements in number theory: easy to say, but.

A The Beal Conjecture states the following

Conclusion