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

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arxiv 2503.02317 v1 pith:ODMGIRME submitted 2025-03-04 math.NT math.CO

Yuhi Kamio This is my paper · ORCID
classification math.NTmath.CO
keywords unitasymptoticcitefractionsproblemanalysiscasedecomposing
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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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  1. Eventually greedy best Egyptian underapproximations of rational numbers via optimal control

    math.NT 2026-07 accept novelty 8.0 of 10

    Every positive rational number has eventually greedy best Egyptian underapproximations, with and without repeated denominators, and a Liouville example with unique greedy best underapproximations is constructed.

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