On a Curious Biconditional Involving Divisors of Odd Perfect Numbers

Jose Arnaldo B. Dris

On a Curious Biconditional Involving Divisors of Odd Perfect Numbers

Number Theory 2018-01-12 v9

Authors: Jose Arnaldo B. Dris

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.

Keywords

odd perfect numbers divisors Dris conjecture Euler prime biconditional inequalities

Cite

@article{arxiv.1309.0906,
  title  = {On a Curious Biconditional Involving Divisors of Odd Perfect Numbers},
  author = {Jose Arnaldo B. Dris},
  journal= {arXiv preprint arXiv:1309.0906},
  year   = {2018}
}

Comments

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

On a Curious Biconditional Involving Divisors of Odd Perfect Numbers

Abstract

Keywords

Cite

Comments

Related papers