On a conjecture of M. N. Bleicher and P. Erdős
type: Item
instance of: scholarly article
title: On a conjecture of M. N. Bleicher and P. Erdős
zbMATH Open document ID: 0589.10018
DOI: 10.1016/0022-314X(86)90060-0
author: H. Yokota
published in: Journal of Number Theory
publication date: 1986-01-01T00:00:00Z
review text: Let \(D(a,N)=\min \{n_ K:\) \(a/N=\sum^{K}_{1}(1/n_ i)\), \(n_ 1<n_ 2<...<n_ K\), \(n_ i\in {\mathbb{Z}}\}\), where minimum ranges over all expansions of a/N, and let \(D(N)=\max \{D(a,N):\quad 1\leq a<N\}.\) The author proves that if \(M\leq N\), then \(D(M N)\leq M D(N),\) and it implies that \(D(M N)\leq \max \{M D(N),\quad N D(M)\}\leq D(M) D(N),\) establishing a conjecture by M. N. Bleicher and P. Erdős.
reviewed by: Xu Guangshan
Mathematics Subject Classification ID: 11D68
zbMATH DE Number: 3946220
zbMATH Keywords: sums of unit fractions
Wikidata QID: Q123332737
MaRDI profile type: Publication
cites work: Denominators of Egyptian fractions
cites work: Denominators of Egyptian fractions. II
cites work: Q3872528
description: scientific article; zbMATH DE number 3946220