A SHORT ELEMENTARY PROOF OF THE BEAL CONJECTURE WITH DEDUCTION OF THE FERMAT LAST THEOREM

Authors

  • Mohammed Ghanim Author

Keywords:

A Diophantine, equation-The Fermat, generalized equation-The Fermat/Catalan, equation-The Beal conjecture, The Fermat last theorem -Primitive integers, The Intermediate value theorem, The L’Hôpital rule, The Bolzano/Weierstrass, theorem -The Catalan/Mihailescu theorem, 2010 Mathematics Subject Classification, 11 A xx (Elementary Number theory).

Abstract

The present short paper, which is an amelioration of my previous article “confirmation of the Beal-BrunTijdeman-Zagier conjecture” published by the GJETS in 20/11/2019 [15], confirms the Beal’s conjecture, remained open since 1914 and saying that: "∃, , ∈ ℕ∗ such that ∶ + = and gcd, , = 1 ⇒ min , !, " = 2" The proof uses elementary tools of mathematics, such as the L’Hôpital rule, the Bolzano-Weierstrass theorem, the intermediate value theorem and the growth properties of certain elementary functions. The proof uses also the Catalan-Mihailescu theorem [18] [19] and some methods developed in my paper on the Fermat last theorem [14] published by the GJAETS in 10/12/2018. The particular case of the Fermat last theorem is deduced.

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Published

2023-07-05

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Articles

How to Cite

A SHORT ELEMENTARY PROOF OF THE BEAL CONJECTURE WITH DEDUCTION OF THE FERMAT LAST THEOREM. (2023). Global Journal of Advanced Engineering Technologies and Sciences, 8(2), 1-16. https://gjaets.com/index.php/gjaets/article/view/10

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