Every real number is a sum of two real numbers with diverging partial quotients
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866911042094759936 |
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| author | Gayfulin, Dmitry Nesharim, Erez |
| author_facet | Gayfulin, Dmitry Nesharim, Erez |
| contents | We show that every irrational number is a sum of two real numbers with diverging partial quotients. The proof is constructive. The key towards these results is an algorithm which was recently developed by Nikita Shulga, and our study of this algorithm is of independent interest. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_04521 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Every real number is a sum of two real numbers with diverging partial quotients Gayfulin, Dmitry Nesharim, Erez Number Theory We show that every irrational number is a sum of two real numbers with diverging partial quotients. The proof is constructive. The key towards these results is an algorithm which was recently developed by Nikita Shulga, and our study of this algorithm is of independent interest. |
| title | Every real number is a sum of two real numbers with diverging partial quotients |
| topic | Number Theory |
| url | https://arxiv.org/abs/2507.04521 |