**Carlos M. da Fonseca and Anthony G. Shannon**

Notes on Number Theory and Discrete Mathematics

Print ISSN 1310–5132, Online ISSN 2367–8275

Volume 30, 2024, Number 3, Pages 491–498

DOI: 10.7546/nntdm.2024.30.3.491-498

**Full paper (PDF, 200 Kb)**

## Details

### Authors and affiliations

Carlos M. da Fonseca

^{1} *Kuwait College of Science and Technology
Doha District, Safat 13133, Kuwait*

^{2}

*Chair of Computational Mathematics, University of Deusto*

48007 Bilbao, Spain

48007 Bilbao, Spain

Anthony G. Shannon

^{3} *Honorary Fellow, Warrane College, University of New South Wales
2033, Australia*

### Abstract

In this note, old and new properties of Fermatian numbers are recalled. A new formal operator is defined and some identities and extensions are discussed.

### Keywords

- Fermatian numbers
- Recurrence relation
- Formal operators

### 2020 Mathematics Subject Classification

- 11B39
- 11B75
- 11B65
- 05A30

### References

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### Manuscript history

- Received: 9 April 2024
- Revised: 16 August 2024
- Accepted: 18 August 2024
- Online First: 26 September 2024

### Copyright information

Ⓒ 2024 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

- Shannon, A. G. (2003). Some Fermatian special functions.
*Notes on Number Theory and Discrete Mathematics*, 9(4), 73–82. - Shannon, A. G. (2004). Some properties of Fermatian numbers.
*Notes on Number Theory and Discrete Mathematics*, 10(2), 25–33. - Shannon, A. G. (2004). A Fermatian Staudt–Clausen Theorem.
*Notes on Number Theory and Discrete Mathematics*, 10(4), 89–99. - Shannon, A. G. (2010). Fermatian analogues of Gould’s generalized Bernoulli polynomials.
*Notes on Number Theory and Discrete Mathematics*, 16(4), 14–17. - Shannon, A. G. (2019). Applications of Mollie Horadam’s generalized integers to Fermatian and Fibonacci numbers.
*Notes on Number Theory and Discrete Mathematics*, 25(2), 113–126.

## Cite this paper

Da Fonseca, C. M., & Shannon, A. G. (2024). A formal operator involving Fermatian numbers. *Notes on Number Theory and Discrete Mathematics*, 30(3), 491-498, DOI: 10.7546/nntdm.2024.30.3.491-498.