On the Form of Odd Perfect Gaussian Integers

TL;DR

This paper extends the sum-of-divisors function to Gaussian integers and proves a modified classification of odd perfect numbers within this complex number framework.

Contribution

It introduces a new extension of the sum-of-divisors function to Gaussian integers and provides a modified classification of odd perfect numbers.

Findings

Extended sum-of-divisors function to Gaussian integers

Proved a modified Euler's classification for odd perfect numbers

Enhanced understanding of perfect numbers in complex integers

Abstract

We extend the sum-of-divisors function to the complex plane via the Gaussian integers. Then we prove a modified form of Euler's classification of odd perfect numbers.