Numbers with three close factorizations

Tsz Ho Chan

arXiv:1303.2249·math.NT·March 15, 2013

Numbers with three close factorizations

Tsz Ho Chan

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TL;DR

This paper investigates numbers that have three distinct factorizations with factors grouped into two close sets, revealing structural properties of such numbers.

Contribution

It introduces a novel analysis of numbers with three close factorizations, expanding understanding of their structural characteristics.

Findings

01

Identifies conditions for numbers with three close factorizations

02

Provides bounds on the size and distribution of such numbers

03

Characterizes the relationships between the factors in these factorizations

Abstract

In this paper, we study numbers $n$ that can be factored in three different ways as $n = A_{1} B_{1} = A_{2} B_{2} = A_{3} B_{3}$ where $A_{1}$ , $A_{2}$ , $A_{3}$ are close to each other and $B_{1}$ , $B_{2}$ , $B_{3}$ are close to each other.

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Taxonomy

Topicsgraph theory and CDMA systems · Mathematics and Applications · Rings, Modules, and Algebras