Jose Arnaldo Bebita Dris and Doli-Jane Uvales Tejada

Notes on Number Theory and Discrete Mathematics

Print ISSN 1310–5132, Online ISSN 2367–8275

Volume 24, 2018, Number 4, Pages 18—25

DOI: 10.7546/nntdm.2018.24.4.18-25

**Download full paper: PDF, 177 Kb**

## Details

### Authors and affiliations

Jose Arnaldo Bebita Dris

*Institute of Mathematics, University of the Philippines
Carlos P. Garcia Avenue, Diliman, Quezon City, Philippines*

Doli-Jane Uvales Tejada

*Mathematics Department, College of Natural Sciences and Mathematics
Mindanao State University, General Santos City, Philippines*

### Abstract

In this note, we revisit and show how some old results on odd perfect numbers follow from assuming some unproven yet reasonable conjectures.

### Keywords

- Odd perfect number
- Descartes–Frenicle–Sorli conjecture
- Dris conjecture
- Abundancy index
- Deficiency

### 2010 Mathematics Subject Classification

- 11A25

### References

- Beasley, B. D. (2013) Euler and the ongoing search for odd perfect numbers, ACMS 19th Biennial Conference Proceedings, Bethel University.
- Brown, P. A. (2016) A partial proof of a conjecture of Dris, preprint, https://arxiv.org/pdf/1602.01591v1.pdf.
- Dickson, L. E. (1971) History of the theory of numbers, Vol. 1, 3–33, Chelsea Pub. Co., New York.
- Dris, J. A. B. (2008) Solving the odd perfect number problem: Some old and new approaches, M. S. Math thesis, De La Salle University, Manila, Philippines.
- Dris, J. A. B. (2009) Solving the odd perfect number problem: Some new approaches, Electr. Proc. of the 11th Science and Technology Congress, ed. L. Pajo, De La Salle University.
- Dris, J. A. B. (2012) The abundancy index of divisors of odd perfect numbers, J. Integ. Seq., 15 (4), Article 12.4.4.
- Dris, J. A. B. (2017) Conditions equivalent to the Descartes–Frenicle–Sorli Conjecture on odd perfect numbers, Notes on Number Theory and Discrete Mathematics, 23 (2), 12–20.
- Dris, J. A. B. (2017) On a curious biconditional involving divisors of odd perfect numbers, Notes on Number Theory and Discrete Mathematics, 23 (4), 1–13.
- Dris, J. A. B., & Luca, F. (2016) A note on odd perfect numbers, Fibonacci Quart., 54 (4), 291–295.
- Mihailescu, P. (2004) Primary cyclotomic units and a proof of Catalan’s Conjecture, J. Reine Angew. Math., 572, 167–195.
- Nielsen, P. (2015) Odd perfect numbers, Diophantine equations, and upper bounds, Math. Comp., 84, 2549–2567.
- Ochem, P., & Rao, M. (2012) Odd perfect numbers are greater than 101500, Math. Comp., 81, 1869–1877.
- Sorli, R. M. (2003) Algorithms in the study of multiperfect and odd perfect numbers, Ph. D. Thesis, University of Technology, Sydney.
- Starni, P. (2018) On Dris conjecture about odd perfect numbers, Notes on Number Theory and Discrete Mathematics, 23 (1), 5–9.

## Related papers

## Cite this paper

APADris, J. A. B., & Tejada, D.-J. U. (2018). Revisiting some old results on odd perfect numbers. *Notes on Number Theory and Discrete Mathematics*, 24(4), 18-25, doi: 10.7546/nntdm.2018.24.4.18-25.

Dris, Jose Arnaldo Bebita and Doli-Jane Uvales Tejada. “Revisiting Some Old Results on Odd Perfect Numbers.” Notes on Number Theory and Discrete Mathematics 24, no. 4 (2018): 18-25, doi: 10.7546/nntdm.2018.24.4.18-25.

MLADris, Jose Arnaldo Bebita and Doli-Jane Uvales Tejada. “Revisiting Some Old Results on Odd Perfect Numbers.” Notes on Number Theory and Discrete Mathematics 24.4 (2018): 18-25. Print, doi: 10.7546/nntdm.2018.24.4.18-25.