On factoring of unlimited integers

TL;DR

This paper investigates the representation of unlimited integers as sums and products of unlimited integers, providing a corrected proof under Dickson's Conjecture and addressing related questions.

Contribution

It offers a corrected proof regarding the sum and product decomposition of unlimited integers assuming Dickson's Conjecture and answers related open questions.

Findings

Under Dickson's Conjecture, not all unlimited integers can be expressed as the sum of a limited and a product of two unlimited integers.

The paper corrects a previous erroneous proof and provides a valid argument.

It addresses additional questions posed by Boudaoud and Bellaouar.

Abstract

A. Boudaoud asked whether every unlimited integer is a sum of a limited integer and a product of two unlimited integers. Assuming Dickson's Conjecture, the answer is negative. The erroneous proof of claim (2) on page 5 of the published version is replaced by a correct one (see pages 6 - 7) and an answer to another question of Boudaoud and Bellaouar is given. \end{abstract}