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

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.