There Are No Odd Perfect Numbers

TL;DR

This paper proves that no odd perfect numbers exist, resolving a long-standing open problem by demonstrating that all perfect numbers must be even.

Contribution

It provides a proof that odd perfect numbers do not exist, settling a major question in number theory.

Findings

Proof that odd perfect numbers do not exist

Clarification of the structure of perfect numbers

Resolution of a long-standing open problem in mathematics

Abstract

While the general form of even perfect numbers is well-known, the existence or non-existence of odd perfect numbers is still an open problem. We address this problem and prove that if a natural number is odd, then it's not perfect.