An Elementary Proof of Fermat’s Last Theorem for Epsilons

Bibek Baran Nag

doi:10.4236/apm.2021.118048

Abstract

The author presents a new approach which is used to solve an important Diophantine problem. An elementary argument is used to furnish another fully transparent proof of Fermat’s Last Theorem. This was first stated by Pierre de Fermat in the seventeenth century. It is widely regarded that no elementary proof of this theorem exists. The author provides evidence to dispel this belief.

Highlights

Define n to be any integer such that n > 1
It is widely regarded that no elementary proof of this theorem exists
The first full proof of Fermat’s Last Theorem was established as being a consequence of the modularity theorem for semistable elliptic curves, which was proved in [3] and [4] by Wiles and Taylor. This was succeeded by the proof of the full modularity theorem which settled a longstanding conjecture formulated by Taniyama, Shimura and Weil

Summary

Introduction

Define n to be any integer such that n > 1. Fermat once claimed to have found proof of this conjecture, and so it was regarded as a theorem. The first full proof of Fermat’s Last Theorem was established as being a consequence of the modularity theorem for semistable elliptic curves, which was proved in [3] and [4] by Wiles and Taylor. This was succeeded by the proof of the full modularity theorem (in [5] [6] [7]) which settled a longstanding conjecture formulated by Taniyama, Shimura and Weil.

Analysis

Conclusion and Discussion