SOME DIOPHANTUS-FERMAT DOUBLE EQUATIONS EQUIVALENT TO FREY’S ELLIPTIC CURVE
Keywords:
Fermat’s Last Theorem, Arithmetic algebraic geometry, Diophantine geometry.
Abstract
In this work I demonstrate that a possible origin of the Frey elliptic curve derives from an appropriate use of the double equations of Diophantus-Fermat and from an isomorphism: a birational application between the double equations and an elliptic curve. From this origin I deduce a Fundamental Theorem which allows an exact reformulation of Fermat’s Last Theorem. A complete proof of this Theorem, consisting of a system of homogeneous ternary quadratic Diophantine equations, is certainly possible also through methods known and discovered by Fermat,in order to solve his extraordinary equation.
Published
2023-12-25
Section
Research Article
Copyright (c) 2023 Journal of Ramanujan Society of Mathematics and Mathematical Sciences
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