On a Curious Biconditional Involving Divisors of Odd Perfect Numbers

Abstract

We investigate the implications of a curious biconditional involving 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.

10 pages - A previous version of this paper was titled "The Abundancy Index of Divisors of Odd Perfect Numbers - Part II", which was co-authored with Keneth Adrian P. Dagal. The present paper supersedes all previous versions

Cited by in corpus (3)

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• On the Descartes-Frenicle-Sorli and Dris Conjectures Regarding Odd Perfect Numbers