Some Results on Analysis and number theory

TL;DR

This paper presents bounds for solutions to quadratic equations, explores twin primes, and applies linear functionals to prove results related to Fermat's Last Theorem, combining number theory and analysis techniques.

Contribution

It introduces new bounds for quadratic solutions, offers insights into twin primes, and employs linear functionals to prove classical theorems, integrating number theory and analysis.

Findings

Bounds for solutions of quadratic equations in two variables.

Results on twin prime numbers.

Application of linear functionals to Fermat's Last Theorem.

Abstract

In this paper we obtain bounds for integer solutions of quadratic polynomials in two variables that represent a natural number. Also we get some results on twin prime numbers. In addition, we use linear functionals to prove some results of the mathematical analysis and the Fermat's last theorem.