Note on the Theory of Perfect Numbers

TL;DR

This paper presents a proof claiming that odd perfect numbers do not exist, addressing a longstanding open problem in number theory and extending the argument to odd multiperfect numbers.

Contribution

It offers a novel proof approach that aims to resolve the centuries-old question about the existence of odd perfect numbers and generalizes to odd multiperfect numbers.

Findings

No odd perfect numbers exist according to the proof.

The proof extends to show odd multiperfect numbers also do not exist.

Addresses a millennia-old open problem in number theory.

Abstract

A perfect number is a number whose divisors add up to twice the number itself. The existence of odd perfect numbers is a millennia-old unsolved problem. This note proposes a proof of the nonexistence of odd perfect numbers. More generally, the same analysis seems to generalize to a proof of the nonexistence of odd multiperfect numbers.