On a problem involving unit fractions
Abstract
Erdős and Graham proposed to determine the number of subsets $S \subseteq \left\{1,2,\dots,n\right\}$ with $\sum_{s \in S} 1/s = 1$ and asked, among other things, whether that number could be as large as $2^{n  o(n)}$. We show that the number of subsets $S \subseteq \left\{1,2,\dots,n\right\}$ with $\sum_{s \in S} 1/s \leq 1$ is smaller than $2^{0.93n}$.
 Publication:

arXiv eprints
 Pub Date:
 March 2024
 DOI:
 10.48550/arXiv.2403.17041
 arXiv:
 arXiv:2403.17041
 Bibcode:
 2024arXiv240317041S
 Keywords:

 Mathematics  Combinatorics