Length and denominators of Egyptian fractions. II
type: Item
instance of: scholarly article
title: Length and denominators of Egyptian fractions. II
zbMATH Open document ID: 0637.10007
DOI: 10.1016/0022-314X(88)90042-X
author: H. Yokota
published in: Journal of Number Theory
publication date: 1988-01-01T00:00:00Z
review text: Using the notations and definitions of part I (see Zbl 0637.10006), and define moreover \[ L(a,N)=\min \left\{k: a/N=\sum^{k}_{i=1}1/n_ i,\;n_ 1<n_ 2<\ldots<n_ k,\;n_ i\in\mathbb Z_ 0\right\}, \] and \[ L(N)=\max \{L(a,N): 1\leq a<N\}. \] In this second paper, the author develops an algorithm which yields \[ L(N)\leq \frac{2 \log N}{\log \log N}\left(1+\frac{2 \log \log \log N}{\log \log N}\right) \] and \[ D(N)\leq N(\log N)^{2+\varepsilon}, \] where \(\varepsilon\to 0\) as \(N\to \infty\).
Mathematics Subject Classification ID: 11D68
Mathematics Subject Classification ID: 11A67
zbMATH DE Number: 4037910
MaRDI profile type: Publication
cites work: Denominators of Egyptian fractions. II
cites work: Q5513725
cites work: On a Problem of Additive Number Theory
cites work: Approximate formulas for some functions of prime numbers
cites work: Integers with consecutive divisors in small ratio
cites work: Denominators of Egyptian fractions
full work available at URL: 0022-314x(88)90042-x
OpenAlex ID: W2026114553
reviewed by: Ke Zhao
description: scientific article; zbMATH DE number 4037910