| Autor: |
Mao, Guo-Shuai, Wen, Chen-Wei |
| Rok vydání: |
2019 |
| Předmět: |
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| Zdroj: |
The Ramanujan Journal(2021) |
| Druh dokumentu: |
Working Paper |
| DOI: |
10.1007/s11139-021-00400-3 |
| Popis: |
In this paper, we prove two supercongruences conjectured by Z.-W. Sun via the Wilf-Zeilberger method. One of them is, for any prime $p>3$, \begin{align*} \sum_{n=0}^{p-1}\frac{6n+1}{256^n}\binom{2n}n^3&\equiv p(-1)^{(p-1)/2}-p^3E_{p-3}\pmod{p^4}. \end{align*} In fact, this supercongruence is a generalization of a supercongruence of van Hamme. |
| Databáze: |
arXiv |
| Externí odkaz: |
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