Some modular considerations regarding odd perfect numbers

College

College of Science

Department/Unit

Mathematics and Statistics Department

Document Type

Article

Source Title

Notes on Number Theory and Discrete Mathematics

Volume

26

Issue

2

First Page

27

Last Page

33

Publication Date

2020

Abstract

Let pkm2 be an odd perfect number with special prime p. In this article, we provide an alternative proof for the biconditional that σ(m2) ≡ 1 (mod 4) holds if and only if p ≡ k (mod 8). We then give an application of this result to the case when σ(m2 )/pk is a square.

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Digitial Object Identifier (DOI)

10.7546/nntdm.2020.26.2.27-33

Disciplines

Mathematics

Keywords

Perfect numbers

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