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arXiv · 1910.00779

Proof of two supercongruences conjectured by Z.-W. Sun

Guo-Shuai Mao·Chen-Wei Wen
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Abstract

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.

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Guo-Shuai Mao, Chen-Wei Wen. 2019-10-17. Proof of two supercongruences conjectured by Z.-W. Sun. https://doi.org/10.1007/s11139-021-00400-3

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