Some Results on Number Theory and Analysis

Cerna Maguiña B.M.; Garcia D.D.L.; Maguiña H.F.; Girlado M.A.T. · Mathematics and Statistics (2022) · DOI: 10.13189/ms.2022.100220

Resumen

In this work we obtain bounds for the sum of the integer solutions of quadratic polynomials of two variables of the form P = (10x + 9)(10y + 9) or P = (10x + 1)(10y + 1) or P = (10x + 7)(10y + 3) where P is a given natural number that ends in one. This allows us to decide the primality of a natural number P that ends in one. Also we get some results on twin prime numbers. In addition, we use special linear functionals defined on a real Hilbert space of dimension n, n ≥ 2, in which the relation is obtained: a1 + a2 + · · · + an = λ[a21 + · · · + a2n], where ai is a real number for i = 1, …, n. When n = 3 or n = 2 we manage to address Fermat’s Last Theorem and the equation x4 + y4 = z4, proving that both equations do not have positive integer solutions. For n = 2, the Cauchy-Schwartz Theorem and Young’s inequality were proved in an original way.

Instituciones: Universidad Nacional Mayor de San Marcos; Universidad Nacional Federico Villarreal; Universidad Nacional Santiago Antúnez de Mayolo