Proof for the Beal Conjecture and a New Proof for Fermat's Last Theorem
Pure and Applied Mathematics Journal
Volume 2, Issue 5, October 2013, Pages: 149-155
Received: Aug. 20, 2013; Published: Sep. 20, 2013
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Author
Leandro Torres Di Gregorio, Souza Marques EngineeringCollege, Rio de Janeiro, Brazil
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Abstract
The Beal Conjecture was formulated in 1997 and presented as a generalization of Fermat's Last Theorem, within the number theory´s field. It states that, for X, Y, Z, n_1, n_2 and n_3 positive integers with n_1, n_2, n_3> 2, if X^(n_1 )+Y^(n_2 )=Z^(n_3 ) then X, Y, Z must have a common prime factor. This article presents the proof for the Beal Conjecture, obtained from the correspondences between the real solutions of the equations in the forms A^2+B^2=C^2, δ^n+γ^n=α^n and X^(n_1 )+Y^(n_2 )=Z^(n_3 ). In addition, a proof for the Fermat's Last Theorem was performed using basic math.
Keywords
Beal Conjecture, Fermat´s Last Theorem, Diophantine Equations, Number Theory, Prime Numbers
To cite this article
Leandro Torres Di Gregorio, Proof for the Beal Conjecture and a New Proof for Fermat's Last Theorem, Pure and Applied Mathematics Journal. Vol. 2, No. 5, 2013, pp. 149-155. doi: 10.11648/j.pamj.20130205.11
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