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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
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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

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AIMS Mathematics
Volume 11 Issue 6,
June 2026
Pages 18835-18844
DOI: 10.3934/math.2026766

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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

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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)