On eventually greedy best underapproximations by Egyptian fractions

被引：0

作者：

Kovac, Vjekoslav ^{[1
]}

机构：

[1] Univ Zagreb, Fac Sci, Dept Math, Bijenicka Cesta 30, Zagreb 10000, Croatia

来源：

JOURNAL OF NUMBER THEORY | 2025年 / 268卷

关键词：

Unit fraction; Underapproximation; Greedy algorithm; Lebesgue measure;

D O I：

10.1016/j.jnt.2024.09.004

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Erd & odblac;s and Graham found it conceivable that the best nterm Egyptian underapproximation of almost every positive number for sufficiently large n gets constructed in a greedy manner, i.e., from the best (n - 1)-term Egyptian underapproximation. We show that the opposite is true: the set of real numbers with this property has Lebesgue measure zero. (c) 2024 Elsevier Inc. All rights are reserved, including those for text and data mining, AI training, and similar technologies.

引用

页码：39 / 48

页数：10

共 18 条

[1]

Bloom T. F., 2022, NIEUW ARCH WISKD, V23, P237

[2]

Bloom Thomas F., Erds problems

[3]

Chu HV, 2024, Arxiv, DOI [arXiv:2306.12564, /10.1016/j.indag.2024.01.006, DOI 10.1016/J.INDAG.2024.01.006]

[4]

Conlon D., arXiv

[5]

CURTISS DR, 1922, AM MATH MONTHLY, V29, P380

[6] Diophantine m-tuples in finite fields and modular forms [J].

Dujella, Andrej ;

Kazalicki, Matija .

RESEARCH IN NUMBER THEORY, 2021, 7 (01)

[7]

Erdos P., 1950, Mat. Lapok, V1, P192

[8]

Erdos P., 1980, OLD NEW PROBLEMS RES

[9]

Graham RL, 2013, BOLYAI SOC MATH STUD, V25, P289

[10]

Green Richard, Egyptian fractions

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