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

Guo-Shuai Mao

doi:10.1016/j.jsc.2025.102545

paper

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

arXiv:2201.06951 · doi:10.1016/j.jsc.2025.102545

Abstract

In this paper, we mainly prove a congruence conjecture of Z.-W. Sun \cite{Sjnt}: Let $p > 5$ be a prime. Then $k = (p + 1) /2 \sum p - 1 \frac{( k 2 k ) ^{2}}{k 1 6 ^{k}} \equiv - \frac{21}{2} H_{p - 1} (mod p^{4}),$ where $H_{n}$ denotes the $n$ -th harmonic number.

19 pages, this is a preliminary draft, comments are welcome. arXiv admin note: text overlap with arXiv:2201.03418

Supercongruences involving products of two binomial coefficients modulo p4

Abstract

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