A question of Erdős and Graham on Egyptian fractions
Fuente:
arXiv
Gespeichert in:
| Hauptverfasser: | , , , , , , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2024
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866908718828879872 |
|---|---|
| author | Conlon, David Fox, Jacob He, Xiaoyu Mubayi, Dhruv Pham, Huy Tuan Suk, Andrew Verstraëte, Jacques |
| author_facet | Conlon, David Fox, Jacob He, Xiaoyu Mubayi, Dhruv Pham, Huy Tuan Suk, Andrew Verstraëte, Jacques |
| contents | Answering a question of Erdős and Graham, we show that for each fixed positive rational number $x$ the number of ways to write $x$ as a sum of reciprocals of distinct positive integers each at most $n$ is $2^{(c_x + o(1))n}$ for an explicit constant $c_x$ increasing with $x$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_16016 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A question of Erdős and Graham on Egyptian fractions Conlon, David Fox, Jacob He, Xiaoyu Mubayi, Dhruv Pham, Huy Tuan Suk, Andrew Verstraëte, Jacques Combinatorics Number Theory Answering a question of Erdős and Graham, we show that for each fixed positive rational number $x$ the number of ways to write $x$ as a sum of reciprocals of distinct positive integers each at most $n$ is $2^{(c_x + o(1))n}$ for an explicit constant $c_x$ increasing with $x$. |
| title | A question of Erdős and Graham on Egyptian fractions |
| topic | Combinatorics Number Theory |
| url | https://arxiv.org/abs/2404.16016 |