Additive properties of even perfect numbers

TL;DR

This paper proves that every integer less than or equal to an even perfect number can be expressed as a sum of its divisors, revealing a new additive property of these special numbers.

Contribution

It establishes a novel additive property of even perfect numbers, showing that all smaller integers can be represented as sums of their divisors.

Findings

Any integer m ≤ n can be expressed as a sum of divisors of n.

The property applies specifically to even perfect numbers.

This enhances understanding of the structure of perfect numbers.

Abstract

A positive integer n is said to be perfect if sigma(n)=2n, where sigma denotes the sum of the divisors of n. In this article, we show that if n is an even perfect number, then any integer m<=n is expressed as a sum of some of divisors of n.