Two new arithmetic operations

Krassimir Atanassov and József Sándor
Notes on Number Theory and Discrete Mathematics
Print ISSN 1310–5132, Online ISSN 2367–8275
Volume 32, 2026, Number 1, Pages 207–213
DOI: 10.7546/nntdm.2026.32.1.207-213
Full paper (PDF, 167 Kb)

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Authors and affiliations

Krassimir Atanassov
Department of Bioinformatics and Mathematical Modelling, Institute of Biophysics and Biomedical Engineering, Bulgarian Academy of Sciences
Acad. G. Bonchev Str., Bl. 105, Sofia-1113, Bulgaria

József Sándor
Department of Mathematics, Babeș-Bolyai University
Str. Kogălniceanu nr. 1, 400084 Cluj-Napoca, Romania

Abstract

Two arithmetic operations are introduced and some of their properties are studied. It is proved that they can be operations of semi-groups, but not of monoids. It is shown that their reverse operations are not one-valued. Some connections between the new operations and the well-known arithmetic functions \varphi, \psi, \sigma are shown.

Keywords

  • Arithmetic function
  • Arithmetic operation
  • Semi-group

2020 Mathematics Subject Classification

  • 11A99

References

  1. Atanassov, K. (2002). Restrictive factor: Definition, properties and problems. Notes on Number Theory and Discrete Mathematics, 8(4), 117–119.
  2. Atanassov, K. (2016). On function “Restrictive factor”. Notes on Number Theory and Discrete Mathematics, 22(2), 17–22.
  3. Panaitopol, L. (2004). Properties of the Atanassov functions. Advanced Studies on Contemporary Mathematics, 8(1), 55–59.
  4. Sándor, J., & Atanassov, K. (2020). Restrictive factor and extension factor. Notes on Number Theory and Discrete Mathematics, 26(2), 34–46.
  5. Sándor, J., & Atanassov, K. (2021). Arithmetic Functions. Nova Sciences, New York.

Manuscript history

  • Received: 3 November 2025
  • Revised: 5 March 2026
  • Accepted: 18 March 2026
  • Online First: 19 March 2026

Copyright information

Ⓒ 2026 by the Authors.
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).

Related papers

  1. Sándor, J., & Atanassov, K. (2020). Restrictive factor and extension factor. Notes on Number Theory and Discrete Mathematics, 26(2), 34–46.
  2. Atanassov, K. (2016). On function “Restrictive factor”. Notes on Number Theory and Discrete Mathematics, 22(2), 17–22.
  3. Panaitopol, L., (2003). Properties of the restrictive factor. Notes on Number Theory and Discrete Mathematics, 9(3), 59–61.
  4. Atanassov, K. (2002). Restrictive factor: Definition, properties and problems. Notes on Number Theory and Discrete Mathematics, 8(4), 117–119.

Cite this paper

Atanassov, K., & Sándor, J. (2026). Two new arithmetic operations. Notes on Number Theory and Discrete Mathematics, 32(1), 207-213, DOI: 10.7546/nntdm.2026.32.1.207-213.

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