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| Main Author: | |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2405.12310 |
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| _version_ | 1866913555467468800 |
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| author | Weisenberg, Desmond |
| author_facet | Weisenberg, Desmond |
| contents | Erdős and Graham asked whether any sparse enough admissible set of natural numbers can be translated into a subset of the primes. By using a greedy construction involving powers of primitive roots, we prove that there exist arbitrarily sparse infinite admissible sets that cannot be translated into a subset of the primes, thus answering this question in the negative. We present three additional constructions as well. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_12310 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Sparse Admissible Sets and a Problem of Erdős and Graham Weisenberg, Desmond Number Theory 11B05 Erdős and Graham asked whether any sparse enough admissible set of natural numbers can be translated into a subset of the primes. By using a greedy construction involving powers of primitive roots, we prove that there exist arbitrarily sparse infinite admissible sets that cannot be translated into a subset of the primes, thus answering this question in the negative. We present three additional constructions as well. |
| title | Sparse Admissible Sets and a Problem of Erdős and Graham |
| topic | Number Theory 11B05 |
| url | https://arxiv.org/abs/2405.12310 |