On a supercongruence conjecture of Z.-W. Sun
| Autor: | Mao, Guo-Shuai |
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| Rok vydání: | 2020 |
| Předmět: | |
| Zdroj: | Chinese Annals of Mathematics, Series B (2022) 43(3), 2022, 417-424 |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1007/s11401-022-0332-7 |
| Popis: | In this paper, we partly prove a supercongruence conjectured by Z.-W. Sun in 2013. Let $p$ be an odd prime and let $a\in\mathbb{Z}^{+}$. Then if $p\equiv1\pmod3$, we have \begin{align*} \sum_{k=0}^{\lfloor\frac{5}6p^a\rfloor}\frac{\binom{2k}k}{16^k}\equiv\left(\frac{3}{p^a}\right)\pmod{p^2}, \end{align*} where $\left(\frac{\cdot}{\cdot}\right)$ is the Jacobi symbol. Comment: 8 pages |
| Databáze: | arXiv |
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