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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/2405.08650 |
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| _version_ | 1866915496207581184 |
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| author | Jain, Vishesh Pham, Huy Tuan Sawhney, Mehtaab Zakharov, Dmitrii |
| author_facet | Jain, Vishesh Pham, Huy Tuan Sawhney, Mehtaab Zakharov, Dmitrii |
| contents | We present an explicit subset $A\subseteq \mathbb{N} = \{0,1,\ldots\}$ such that $A + A = \mathbb{N}$ and for all $\varepsilon > 0$, \[\lim_{N\to \infty}\frac{\big|\big\{(n_1,n_2): n_1 + n_2 = N, (n_1,n_2)\in A^2\big\}\big|}{N^{\varepsilon}} = 0.\] This answers a question of Erdős. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_08650 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | An explicit economical additive basis Jain, Vishesh Pham, Huy Tuan Sawhney, Mehtaab Zakharov, Dmitrii Combinatorics We present an explicit subset $A\subseteq \mathbb{N} = \{0,1,\ldots\}$ such that $A + A = \mathbb{N}$ and for all $\varepsilon > 0$, \[\lim_{N\to \infty}\frac{\big|\big\{(n_1,n_2): n_1 + n_2 = N, (n_1,n_2)\in A^2\big\}\big|}{N^{\varepsilon}} = 0.\] This answers a question of Erdős. |
| title | An explicit economical additive basis |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2405.08650 |