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Some Modular Considerations Regarding Odd Perfect Numbers

EasyChair Preprint no. 2814

7 pagesDate: February 29, 2020

Abstract

Let $p^k m^2$ be an odd perfect number with special prime $p$. In this article, we provide an alternative proof for the biconditional that $\sigma(m^2) \equiv 1 \pmod 4$ holds if and only if $p \equiv k \pmod 8$. We then give an application of this result to the case when $\sigma(m^2)/p^k$ is a square.

Keyphrases: Deficiency, Odd perfect number, Special prime, Sum of aliquot divisors, Sum of divisors

BibTeX entry
BibTeX does not have the right entry for preprints. This is a hack for producing the correct reference:
@Booklet{EasyChair:2814,
  author = {Jose Arnaldo Bebita Dris and Immanuel Tobias San Diego},
  title = {Some Modular Considerations Regarding Odd Perfect Numbers},
  howpublished = {EasyChair Preprint no. 2814},

  year = {EasyChair, 2020}}
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