The origin of the Frey elliptic curve in a too narrow margin

TL;DR

This paper explores how Diophantus's double equations lead to the origin of the Frey elliptic curve, offering an elementary proof of Fermat's Last Theorem.

Contribution

It demonstrates the historical and mathematical connection between Diophantus's equations and the Frey elliptic curve, providing a new perspective on Fermat's Last Theorem.

Findings

Identifies the origin of the Frey elliptic curve in Diophantus's work

Provides an elementary proof of Fermat's Last Theorem based on this connection

Highlights the historical significance of double equations in elliptic curve theory

Abstract

It is shown that an appropriate use of so-called double equations by Diophantus provides the origin of the Frey elliptic curve and from it we can deduce an elementary proof of Fermat's Last Theorem.