Cyclotomic Congruences and Lucas Sequences
Fuente:
arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866908752218685440 |
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| author | Ross, Tyler Shen, Zhongyan Cai, Tianxin |
| author_facet | Ross, Tyler Shen, Zhongyan Cai, Tianxin |
| contents | In this paper, we extend the $p$-adic valuations originally obtained by Carmichael for the sequences obtained by applying Möbius inversion to Lucas sequences to $p$-adic congruences, from which we immediately derive corresponding congruences for Lucas sequences. As a corollary, we also establish some constraints on the entry point behavior of primes in Lucas sequences, on the basis of which we conjecture the presence of a strong Chebyshev-like bias in real regular Lucas sequences. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_03468 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Cyclotomic Congruences and Lucas Sequences Ross, Tyler Shen, Zhongyan Cai, Tianxin Number Theory 11B50 (Primary), 11B39 (Secondary) In this paper, we extend the $p$-adic valuations originally obtained by Carmichael for the sequences obtained by applying Möbius inversion to Lucas sequences to $p$-adic congruences, from which we immediately derive corresponding congruences for Lucas sequences. As a corollary, we also establish some constraints on the entry point behavior of primes in Lucas sequences, on the basis of which we conjecture the presence of a strong Chebyshev-like bias in real regular Lucas sequences. |
| title | Cyclotomic Congruences and Lucas Sequences |
| topic | Number Theory 11B50 (Primary), 11B39 (Secondary) |
| url | https://arxiv.org/abs/2512.03468 |