Partial Lucas-type congruences
Fuente:
arXiv
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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866909882940129280 |
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| author | Straub, Armin |
| author_facet | Straub, Armin |
| contents | In their study of a binomial sum related to Wolstenholme's theorem, Chamberland and Dilcher prove that the corresponding sequence modulo primes $p$ satisfies congruences that are analogous to Lucas' theorem for the binomial coefficients with the notable twist that there is a restriction on the $p$-adic digits. We prove a general result that shows that similar partial Lucas congruences are satisfied by all sequences representable as the constant terms of the powers of a multivariate Laurent polynomial. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_01174 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Partial Lucas-type congruences Straub, Armin Number Theory In their study of a binomial sum related to Wolstenholme's theorem, Chamberland and Dilcher prove that the corresponding sequence modulo primes $p$ satisfies congruences that are analogous to Lucas' theorem for the binomial coefficients with the notable twist that there is a restriction on the $p$-adic digits. We prove a general result that shows that similar partial Lucas congruences are satisfied by all sequences representable as the constant terms of the powers of a multivariate Laurent polynomial. |
| title | Partial Lucas-type congruences |
| topic | Number Theory |
| url | https://arxiv.org/abs/2511.01174 |