Abstract
In this research, a proof of Beal’s conjecture is presented. A possible Pythagorean algebraic relationship between the terms of the conjecture problem will be proposed and used to arrive at the proof results. In the process of seeking the proof the solution of the congruent number problem through a family of cubic curves will be discussed. Key words: Proof of Beal’s conjecture, proof of ABC conjecture, algebraic proof of Fermat’s last theorem, the congruent number problem, rational points on the elliptic curve, Pythagorean triples
Highlights
Beal’s conjecture was formulated in 1993 by Andrew Beal, a banker and amateur mathematician while investigating generalizations of Fermat’s last theorem
A relationship has been established between the terms of a Pythagorean triple
The technique used in proving Beal conjecture can be used to solve problems in number theory, arithmetic of elliptic of elliptic curves etc. (Elkies, 2007)
Summary
A proof of Beal’s conjecture is presented. A possible Pythagorean algebraic relationship between the terms of the conjecture problem will be proposed and used to arrive at the proof results. In the process of seeking the proof the solution of the congruent number problem through a family of cubic curves will be discussed
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