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arXiv · 1909.13173

Proof of some supercongruences via the Wilf-Zeilberger method

Guo-Shuai Mao
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Abstract

In this paper, we prove some supercongruences via the Wilf-Zeilberger method. For instance, for any odd prime $p$ and positive integer $r$ and $\delta\in\{1,2\}$, we have \begin{align*} \sum_{n=0}^{(p^r-1)/\delta} \frac{\left(\frac12\right)^5_n}{n!^5}(10n^2+6n+1)(-4)^n &\equiv\begin{cases}p^{2r}\ \pmod{p^{r+4}} &\tt{if}\ r\leq4, \\0\ \pmod{p^{r+4}} &\tt{if}\ r \geq5. \end{cases} \end{align*}

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Guo-Shuai Mao. 2019-09-29. Proof of some supercongruences via the Wilf-Zeilberger method. https://doi.org/10.1080/10236198.2020.1854239

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