Jose Arnaldo B. Dris

Notes on Number Theory and Discrete Mathematics

Print ISSN 1310–5132, Online ISSN 2367–8275

Volume 23, 2017, Number 4, Pages 1–13

**Full paper (PDF, 177 Kb)**

## Details

### Authors and affiliations

Jose Arnaldo B. Dris

*University of the Philippines-Diliman
*

### Abstract

We investigate the implications of a curious biconditional involving the divisors of odd perfect numbers, if Dris conjecture that *q ^{k}* <

*n*holds, where

*q*

^{k}n^{2}is an odd perfect number with Euler prime

*q*. We then show that this biconditional holds unconditionally. Lastly, we prove that the inequality

*q*<

*n*holds unconditionally.

### Keywords

- Odd perfect number
- Abundancy index
- Deficiency

### AMS Classification

- 11A25

### References

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*Notes on Number Theory and Discrete Mathematics*, 23(2), 12–20. - Dris, J. A. B. (2017) New results for the Descartes–Frenicle–Sorli conjecture on odd perfect numbers, Journal for Algebra and Number Theory Academia, 6(3), 95–114.
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## Related papers

- Dris, J. A. B., & San Diego, I. T. (2020). Some modular considerations regarding odd perfect numbers – Part II.
*Notes on Number Theory and Discrete Mathematics*, 26 (3), 8-24. - Dagal, K. A. P., & Dris, J. A. B. (2021). The abundancy index of divisors of odd perfect numbers – Part II.
*Notes on Number Theory and Discrete Mathematics*, 27(2), 12-19.

## Cite this paper

Dris, J. A. B. (2017). On a Curious Biconditional Involving the Divisors of Odd Perfect Numbers. *Notes on Number Theory and Discrete Mathematics*, 23(4), 1-13.