Gardado en:
| Main Authors: | , |
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| Formato: | Preprint |
| Publicado: |
2024
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| Subjects: | |
| Acceso en liña: | https://arxiv.org/abs/2404.07113 |
| Tags: |
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Table of 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.