June 11, 2024Open Access

On eventually greedy best underapproximations by Egyptian fractions

Key Points

Key points are not available for this paper at this time.

Abstract

Erdos and Graham found it conceivable that the best n-term 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. This note solves Problem 206 on Bloom's website "Erdos problems".

Read Full Paperexternally

Bookmark

View Full Paper

Cite This Study

Vjekoslav Kovač (Tue,) studied this question.

synapsesocial.com/papers/68e65550b6db6435875e4861 https://doi.org/https://doi.org/10.48550/arxiv.2406.07218

Also Consider

Synapse has enriched 5 closely related papers on similar clinical questions. Consider them for comparative context:

1A lower bound for the number of Egyptian fractions2025
2The Best Two-Term Underapproximation Using Numbers From Fibonacci-Type Sequences2025
3A question of Erdős and Graham on Egyptian fractions2024
4Sparse Admissible Sets and a Problem of Erdős and Graham2024
5On a problem of Erdős and Graham about consecutive sums in strictly increasing sequences2024

Bookmark

View Full Paper