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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2404.07113 |
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| _version_ | 1866913308705030144 |
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| author | Liu, Yang P. Sawhney, Mehtaab |
| author_facet | Liu, Yang P. Sawhney, Mehtaab |
| contents | We prove that a subset $A\subseteq [1, N]$ with \[\sum_{n\in A}\frac{1}{n} \ge (\log N)^{4/5 + o(1)}\] contains a subset $B$ such that \[\sum_{n\in B} \frac{1}{n} = 1.\] Our techniques refine those of Croot and of Bloom. Using our refinements, we additionally consider a number of questions regarding unit fractions due to Erdős and Graham. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_07113 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On further questions regarding unit fractions Liu, Yang P. Sawhney, Mehtaab Number Theory We prove that a subset $A\subseteq [1, N]$ with \[\sum_{n\in A}\frac{1}{n} \ge (\log N)^{4/5 + o(1)}\] contains a subset $B$ such that \[\sum_{n\in B} \frac{1}{n} = 1.\] Our techniques refine those of Croot and of Bloom. Using our refinements, we additionally consider a number of questions regarding unit fractions due to Erdős and Graham. |
| title | On further questions regarding unit fractions |
| topic | Number Theory |
| url | https://arxiv.org/abs/2404.07113 |