On a Special Case of Dirichlet's Theorem

Jhixon Macías

On a Special Case of Dirichlet's Theorem

General Mathematics 2023-11-21 v1

Authors: Jhixon Macías

Abstract

Let $p$ be a prime number, and $h$ a positive integer such that $\gcd(p,h)=1$ . We prove, without invoking Dirichlet's theorem, that the arithmetic progression $p\left(\mathbf{N}\cup \{0\}\right)+h$ contains infinitely many prime numbers. This is a special case of Dirichlet's theorem not considered by other authors.

Keywords

dirichlet's theorem arithmetic progression prime numbers special case elementary proof

Cite

@article{arxiv.2311.11946,
  title  = {On a Special Case of Dirichlet's Theorem},
  author = {Jhixon Macías},
  journal= {arXiv preprint arXiv:2311.11946},
  year   = {2023}
}

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