Preprint / Version 1

Sum of proper divisors: a general algebraic identity and perfect numbers

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Imanol Urcola Sin afiliación https://orcid.org/0009-0002-7999-103X

DOI:

https://doi.org/10.1590/SciELOPreprints.18161

Keywords:

perfect numbers, sigma function, Euclid-Euler Theorem, proper divisors, algebraic identity

Abstract

In this article, a general algebraic identity for the sum of the proper divisors of every integer greater than one is proposed. Using this identity and some auxiliary results, it has been proved that all perfect numbers have the form described by the Euclid-Euler Theorem.

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Submitted

09/24/2026

Posted

09/25/2026

How to Cite

Sum of proper divisors: a general algebraic identity and perfect numbers. (2026). In SciELO Preprints. https://doi.org/10.1590/SciELOPreprints.18161