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arXiv · 2201.06951

Supercongruences involving products of two binomial coefficients modulo $p^4$

Guo-Shuai Mao
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Abstract

In this paper, we mainly prove a congruence conjecture of Z.-W. Sun \cite{Sjnt}: Let $p>5$ be a prime. Then $$ \sum_{k=(p+1)/2}^{p-1}\frac{\binom{2k}k^2}{k16^k}\equiv-\frac{21}2H_{p-1}\pmod{p^4}, $$ where $H_n$ denotes the $n$-th harmonic number.

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Guo-Shuai Mao. 2022-03-31. Supercongruences involving products of two binomial coefficients modulo $p^4$. https://doi.org/10.1016/j.jsc.2025.102545

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