El teorema de Dirichlet, la conjetura de Goldbach y algunas consecuencias

TL;DR

This paper explores the Dirichlet theorem, simplifies and generalizes it, discusses its relation to Bertrand's postulate, and deduces the Goldbach conjecture's validity, presenting new related results.

Contribution

It provides a simplified and generalized version of Dirichlet's theorem and establishes a connection with the Goldbach conjecture, offering new insights and results.

Findings

Equivalence between Dirichlet's theorem and Bertrand's postulate

Deduction of Goldbach conjecture's validity

Additional results derived from Goldbach's conjecture

Abstract

In this article we study in depth the Dirichlet theorem, which states that if a, b are relative prime integers, the sequence p = an + b contains infinite prime numbers, we simplify and generalize this theorem, we enunciate some special theorems (from Elias), we see equivalence with Bertrand's postulate and we deduce the validity of the Goldbach conjecture. Finally we enunciate some additional results that are deduced from the conjecture-theorem of Goldbach-