Demonstration for Fermat’s last theorem and Beal’s conjecture
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Pythagorean Theorem, Fermat’s Last Theorem, Beal Conjecture Classification AMS: 11D41Abstract
Fermat’s Last Theorem (FLT), 1637, states that if n is an integer greater than 2, then it is impossible to find three positive integer numbers x, y and z in xn yn zn where such equality is met being (x,y) coprime. Beal’s Conjecture (BC), 1993, states that in equation Ax + By Cz , where (A,B,C,x, y,z) and (x, y,z)>2 are different exponents, then (A,B,C) must have a prime factor, for positive integer solutions, but if are coprime and the exponents (x, y,z)>2 are different, there are no positive integer solutions. The present proof contains two theorems that finally allow us to demonstrate the Beal Conjecture, transforming the equation of Beal conjecture into the form of Fermat’s Last Theorem equation. Since there are no solutions in positive integer numbers for Fermat’s Last Theorem equation, then the Beal’s Conjecture does not have solution in positive integer numbers for unequal exponents or with two equal exponents, but all greater than two, being two of their bases coprime.
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