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arXiv · 1302.5991

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

Jose Arnaldo B. Dris
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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 $q^2 < n$.

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Jose Arnaldo B. Dris. 2013-02-25. New Results for the Descartes-Frenicle-Sorli Conjecture on Odd Perfect Numbers. https://arxiv.org/abs/1302.5991

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