Algebra

2309 Submissions

[2] viXra:2309.0097 [pdf] submitted on 2023-09-19 20:59:07

Proof of Beal's Conjecture

Authors: Vedernikov Sergey Ivanovich
Comments: 11 Pages. In Russian

Применение некоторых моментов, не имеющих распространения в современной алгебре и теории чисел, по крайней мере в справочной литературе, для доказательства теоремы Ферма и гипотезы Била.

The purpose of this work is to prove Beal's conjecture. The proof is based on methods not currently used by elementary mathematics. The concept of them is absent in the reference sources. Firstly, this is an idea of the possibility of expressing an even number that has a factor of 8 by the difference of the squares oftwo odd numbers. In addition, a feature of the integer solution of the quadratic equation by Pythagorean triples is applied. As a result, Beale's conjecture was completely proved, taking into account the accompanying Fermat's Last Theorem, by simple methods. Keywords: difference of squares of two odd numbers, factorization, even numbers, odd numbers, Pythagorean triples.
Category: Algebra

[1] viXra:2309.0024 [pdf] submitted on 2023-09-05 02:48:29

Calculation of Nth Partial Sums ���� of Power Series and Its Relationship with the Calculation of Bernoulli Numbers

Authors: Carlos Oscar Rodríguez Leal
Comments: 2 Pages. In Spanish

In this work, the general formula of the n-th partial sums ��_n of sums of powers of the form 1^n+ 2^n + . . . + m^n is obtained by an algebraic method, and said formula is applied to the obtaining the Bernoulli numbers by a new simple method.

En este trabajo se obtiene la fórmula general de las n-ésimas sumas parciales ��^n de sumas de potencias de la forma 1^n + 2^n + . . . + m^n mediante un método algebraico y dicha fórmula se aplica a la obtención de los números de Bernoulli por un método alternativo recursivo sencillo.
Category: Algebra