**A. M. S. Ramasamy**

Notes on Number Theory and Discrete Mathematics

Print ISSN 1310–5132, Online ISSN 2367–8275

Volume 30, 2024, Number 2, Pages 236–252

DOI: 10.7546/nntdm.2024.30.2.236-252

**Full paper (PDF, 284 Kb)**

## Details

### Authors and affiliations

A. M. S. Ramasamy

*Department of Mathematics, Pondicherry University
Pondicherry – 605014, India
*

### Abstract

Let be an odd prime In Part I, starting from an -cycle in a finite field , we have established how the divisors of Mersenne, Fermat and Lehmer numbers arise. The converse question is taken up in this Part with the introduction of an arithmetic function and the notion of a split-associated prime.

### Keywords

*M*-cycle- Jacobi symbol
- Arithmetic function
- Split-associated prime
- Root point

### 2020 Mathematics Subject Classification

- 11A25
- 11A41
- 11B50
- 11C08
- 11T06
- 11T30

### References

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### Manuscript history

- Received: 25 August 2023
- Revised: 16 March 2024
- Accepted: 26 March 2024
- Online First: 8 May 2024

### Copyright information

Ⓒ 2024 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).

## Related papers

- Leyendekkers, J. V., & Shannon, A. G. (2005). Fermat and Mersenne numbers.
*Notes on Number Theory and Discrete Mathematics*, 11(4), 17–24. - Ramasamy, A. M. S. (2024). Sequences in finite fields yielding divisors of Mersenne, Fermat and Lehmer numbers, I.
*Notes on Number Theory and Discrete Mathematics*, 30(1), 116–140.

## Cite this paper

Ramasamy, A. M. S. (2024). Sequences in finite fields yielding divisors of Mersenne, Fermat and Lehmer numbers, II. *Notes on Number Theory and Discrete Mathematics*, 30(2), 236-252, DOI: 10.7546/nntdm.2024.30.2.236-252.