New Results for the Descartes-Frenicle-Sorli Conjecture on Odd Perfect Numbers

Abstract

If $N=q^k{n}^2$ is an odd perfect number given in Eulerian form, then the Descartes-Frenicle-Sorli conjecture predicts that $k=1$. Brown has recently announced a proof for the inequality $q<n$, and a partial proof that $q^k<n$ holds under many cases. In this article, we give a strategy for strengthening Brown's result to $q^2<n$.

arXiv comment17 pages

References in corpus (1)

• Solving the Odd Perfect Number Problem: Some Old and New Approaches

Cited by in corpus (2)

• On a Curious Biconditional Involving Divisors of Odd Perfect Numbers
• Euclid-Euler Heuristics for Perfect Numbers