Integers representable as the product of the sum of four integers with the sum of their reciprocals

TL;DR

This paper uses elliptic curve theory to analyze which integers can be expressed as the product of the sum of four integers and the sum of their reciprocals, providing conditions for positive representations.

Contribution

It introduces a novel application of elliptic curves to characterize integers with positive representations in this specific form.

Findings

Identifies a sufficient condition for positive integer representations

Connects elliptic curve theory with additive number theory

Provides a framework for further exploration of reciprocal sum representations

Abstract

By the theory of elliptic curves, we study the integers representable as the product of the sum of four integers with the sum of their reciprocals and give a sufficient condition for the integers with a positive representation.