New properties of divisors of natural number

Hamilton Brito da Silva
Notes on Number Theory and Discrete Mathematics
Print ISSN 1310–5132, Online ISSN 2367–8275
Volume 29, 2023, Number 2, Pages 276–283
DOI: 10.7546/nntdm.2023.29.2.276-283
Full paper (PDF, 298 Kb)

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Authors and affiliations

Hamilton Brito da Silva
Instituto Federal de Educação, Ciência e Tecnologia do Pará
Avenida Almirante Barroso, 1155, Brasil

Abstract

The divisors of a natural number are very important for several areas of mathematics, representing a promising field in number theory. This work sought to analyze new relations involving the divisors of natural numbers, extending them to prime numbers. These are relations that may have an interesting application for counting the number of divisors of any natural number and understanding the behavior of prime numbers. They are not a primality test, but they can be a possible tool for this and could also be useful for understanding the Riemann’s zeta function that is strongly linked to the distribution of prime numbers.

Keywords

• Natural number
• Number theory
• Divisors

2020 Mathematics Subject Classification

• 11N64

References

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Manuscript history

• Received: 26 September 2022
• Revised: 14 April 2023
• Accepted: 26 April 2023
• Online First: 1 May 2023

Copyright information

Ⓒ 2023 by the Author.
This is an Open Access paper distributed under the terms and conditions of the Creative Commons Attribution 4.0 International License (CC BY 4.0).