Asymptotic Analysis of Infinite Decompositions of a Unit Fraction into Unit Fractions

Paul Erd\H{o}s posed a problem on the asymptotic estimation of decomposing 1 into a sum of infinitely many unit fractions in \cite{Erd80}. We point out that this problem can be solved in the same way as the finite case, as shown in \cite{Sou05}.

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ArXiv.org
Published
2025-03-04
Primary Topic
Mathematical Approximation and Integration
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article

Asymptotic Analysis of Infinite Decompositions of a Unit Fraction into Unit Fractions

Yuhi Kamio
ArXiv.org
Mathematical Approximation and Integration
article

Asymptotic Analysis of Infinite Decompositions of a Unit Fraction into Unit Fractions

Yuhi Kamio
article en

Abstract

Paul Erd\H{o}s posed a problem on the asymptotic estimation of decomposing 1 into a sum of infinitely many unit fractions in \cite{Erd80}. We point out that this problem can be solved in the same way as the finite case, as shown in \cite{Sou05}.

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Mathematical Approximation and Integration
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Asymptotic Analysis of Infinite Decompositions of a Unit Fraction into Unit Fractions — Yuhi Kamio · ArXiv.org (2025) | TGRS Research Map | TGRS