AI Chat Paper
Note: Please note that the following content is generated by AMiner AI. SciOpen does not take any responsibility related to this content.
{{lang === 'zh_CN' ? '文章概述' : 'Summary'}}
{{lang === 'en_US' ? '中' : 'Eng'}}
Chat more with AI
Powered by AMiner. Clicking this button will take you away from SciOpen.
Home AIMS Mathematics Article
PDF (356.8 KB)
Cite
EndNote(RIS) BibTeX
Collect
Submit Manuscript AI Chat Paper
Show Outline
Outline
Show full outline
Hide outline
Outline
Show full outline
Hide outline
Research Article | Open Access

A generalization of a theorem of Erdős and Niven

Jun Qiu1( ), Hongguang Wu2
School of Big Data and Statistics, Tongling University, Tongling 244000, China
Department of Mathematics, Changzhou University, Changzhou 213164, China
Show Author Information

Abstract

In 1946, Erdős and Niven proved that no two distinct partial sums of the harmonic series can be equal. In this paper, we extend their result by establishing the analogous property for a generalized harmonic series of the form ∑ 1 a + i b , where a and b are coprime positive integers with a > b ≥ 1.

Keywords

harmonic seriesgeneralized harmonic seriespartial sums
CLC number: 11B75, 11B83, 11Y70

References

【1】
【1】
 
 
Crossref Google Scholar
AIMS Mathematics
Volume 11 Issue 6,
June 2026
Pages 18835-18844
DOI: 10.3934/math.2026766

{{item.num}}

Comments on this article

Go to comment

< Back to all reports

Review Status: {{reviewData.commendedNum}} Commended , {{reviewData.revisionRequiredNum}} Revision Required , {{reviewData.notCommendedNum}} Not Commended Under Peer Review

Review Comment

Cite this Report
Close
Close
Cite this article:
Qiu J, Wu H. A generalization of a theorem of Erdős and Niven. AIMS Mathematics, 2026, 11(6): 18835-18844. https://doi.org/10.3934/math.2026766

2

Views

0

Downloads

0

Crossref

0

Web of Science

0

Scopus
Received: 28 April 2026
Revised: 04 June 2026
Accepted: 11 June 2026
Published: 15 June 2026
©2026 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0)