Jose Arnaldo Bebita Dris and Immanuel Tobias San Diego

Notes on Number Theory and Discrete Mathematics

Print ISSN 1310–5132, Online ISSN 2367–8275

Volume 26, 2020, Number 4, Pages 33—38

DOI: 10.7546/nntdm.2020.26.4.33-38

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## Details

### Authors and affiliations

Jose Arnaldo Bebita Dris

*M. Sc. Graduate, Mathematics Department
De La Salle University, Manila, Philippines 1004
*

Immanuel Tobias San Diego

*Department of Mathematics and Physical Sciences
Trinity University of Asia, Quezon City, Philippines 1102
*

### Abstract

We prove that is not a square, if is an odd perfect number with special prime , under the hypothesis that is a square. We are also able to prove the same assertion without this hypothesis. We also show that this hypothesis is incompatible with the set of assumptions We end by stating some conjectures.

### Keywords

- Sum of divisors
- Sum of aliquot divisors
- Deficiency
- Odd perfect number
- Special prime

### 2010 Mathematics Subject Classification

- 11A05
- 11A25

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## Related papers

## Cite this paper

Dris, J. A. B., & San Diego, I. T. (2020). On the quantity *m*^{2} − *p ^{k}* where

*p*

^{k}m^{2}is an odd perfect number, 26(4), 33-38, doi: 10.7546/nntdm.2020.26.4.33-38.