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arXiv · 2109.09877

Proof of a conjectural supercongruence modulo $p^5$

Guo-Shuai Mao·Zhi-Wei Sun
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Abstract

In this paper we prove the supercongruence $$\sum_{n=0}^{(p-1)/2}\frac{6n+1}{256^n}\binom{2n}n^3\equiv p(-1)^{(p-1)/2}+(-1)^{(p-1)/2}\frac{7}{24}p^4B_{p-3}\pmod{p^5}$$ for any prime $p>3$, which was conjectured by Sun in 2019.

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Guo-Shuai Mao, Zhi-Wei Sun. 2021-09-20. Proof of a conjectural supercongruence modulo $p^5$. https://arxiv.org/abs/2109.09877

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