On a problem of Erdös
type: Item
instance of: scholarly article
title: On a problem of Erdös
zbMATH Open document ID: 0876.11006
author: Csaba Sándor
published in: Journal of Number Theory
publication date: 1997-12-03T00:00:00Z
review text: A generalized version of a problem of P. Erdös is solved in the paper. If \(1< a_1< \cdots <a_s\) are positive integers and \(\sum^s_{i=1} a_i^{-1}<n\) then this sum cannot split into \(n\) parts in such a manner that all partial sums are \(\leq 1\). If \(\sum^s_{i=1} a_i^{-1} <n (1-e^{1-n})\) then the mentioned decomposition is possible.
reviewed by: Tibor Šalát
Mathematics Subject Classification ID: 11B75
zbMATH DE Number: 1011049
zbMATH Keywords: sums of inverses of integers
zbMATH Keywords: decomposition
zbMATH Keywords: partial sums
MaRDI profile type: Publication
full work available at URL: jnth.1997.2113
OpenAlex ID: W1987083437
cites work: Q3872528
DOI: 10.1006/JNTH.1997.2113
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description: scientific article; zbMATH DE number 1011049