On the number of solutions of the Diophantine equation \(\sum_{i=1}^n\frac{1}{i}=1\)
type: Item
instance of: scholarly article
title: On the number of solutions of the Diophantine equation \(\sum_{i=1}^n\frac{1}{i}=1\)
zbMATH Open document ID: 1047.11031
published in: Periodica Mathematica Hungarica
publication date: 2004-09-08T00:00:00Z
review text: For each positive integer \(n\) put \(K(n)=\#\{(x_1,\dots,x_n) : \sum_{i=1}^n {{1}\over {x_i}} = 1\}\), where the \(x_i\) denote positive integers. The author shows that we have \(e^{c{{n^3}\over {\log n}}}<K(n)<c_0^{(1+\varepsilon)2^{n-1}}\) for large \(n\). This result improves the bounds given by Erdős, Graham and Strauss.
reviewed by: Lajos Hajdu
Mathematics Subject Classification ID: 11D68
zbMATH DE Number: 2099952
zbMATH Keywords: sum of unit fractions
zbMATH Keywords: Egyptian fractions
author: Csaba Sándor
MaRDI profile type: Publication
cites work: Q3872528
cites work: Q4312862
cites work: Egyptian Fractions
full work available at URL: b:mahu.0000010822.30987.e7
OpenAlex ID: W2000621515
DOI: 10.1023/B:MAHU.0000010822.30987.E7
description: scientific article; zbMATH DE number 2099952