A Generalized Supercongruence of Z.-W. Sun
Fuente:
arXiv
Enregistré dans:
| Auteur principal: | |
|---|---|
| Format: | Preprint |
| Publié: |
2026
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866912973773078528 |
|---|---|
| author | Qi, Wei-Wei |
| author_facet | Qi, Wei-Wei |
| contents | In this paper, we employ the Wilf-Zeilberger (WZ) method to prove a supercongruence conjecture posed by Z.-W. Sun: for any prime $p$, \begin{align*} \sum_{k=0}^{\frac{p-3}{2}}\frac{92k^2+61k+9}{(2k+1)64^k}{2k \choose k}{3k \choose k}{4k \choose 2k}\equiv 6p+16p^2\left(\frac{-1}{p}\right) \pmod{p^3}, \end{align*} where $\left(\frac{\cdot}{p}\right)$ denotes the Legendre symbol. Our proof relies on combinatorial identities and symbolic summation techniques. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_18463 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A Generalized Supercongruence of Z.-W. Sun Qi, Wei-Wei Combinatorics In this paper, we employ the Wilf-Zeilberger (WZ) method to prove a supercongruence conjecture posed by Z.-W. Sun: for any prime $p$, \begin{align*} \sum_{k=0}^{\frac{p-3}{2}}\frac{92k^2+61k+9}{(2k+1)64^k}{2k \choose k}{3k \choose k}{4k \choose 2k}\equiv 6p+16p^2\left(\frac{-1}{p}\right) \pmod{p^3}, \end{align*} where $\left(\frac{\cdot}{p}\right)$ denotes the Legendre symbol. Our proof relies on combinatorial identities and symbolic summation techniques. |
| title | A Generalized Supercongruence of Z.-W. Sun |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2603.18463 |