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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/2412.04632 |
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| _version_ | 1866917981682925568 |
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| author | Jha, Abhishek |
| author_facet | Jha, Abhishek |
| contents | We obtain a totient analogue for Linnik's theorem in arithmetic progressions. Specifically, for any coprime pair of positive integers $(m,a)$ such that $m$ is odd, there exists $n\le m^{2+o(1)}$ such that $φ(n)\equiv a\,\mathrm{mod}\,{m}$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_04632 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Smallest totient in a residue class Jha, Abhishek Number Theory 11B50, 11L40 (Primary) 11N64 (Secondary) We obtain a totient analogue for Linnik's theorem in arithmetic progressions. Specifically, for any coprime pair of positive integers $(m,a)$ such that $m$ is odd, there exists $n\le m^{2+o(1)}$ such that $φ(n)\equiv a\,\mathrm{mod}\,{m}$. |
| title | Smallest totient in a residue class |
| topic | Number Theory 11B50, 11L40 (Primary) 11N64 (Secondary) |
| url | https://arxiv.org/abs/2412.04632 |