Proof of a conjectural supercongruence modulo p⁵

2021/09/20 by Guo-Shuai Mao, Zhi‐Wei Sun, Mao, Guo-Shuai +1
Mathematics · #Advanced Mathematical Identities #Analytic Number Theory Research #Advanced Algebra and Geometry

paper · pdf · doi:10.48550/arxiv.2109.09877

Abstract

In this paper we prove the supercongruence ∑_n=0^(p-1)/2(6n+1)/(256ⁿ)\binom2nn³≡ p(-1)^(p-1)/2+(-1)^(p-1)/2(7)/(24)p⁴B_p-3\pmodp⁵ for any prime p>3, which was conjectured by Sun in 2019.

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