Supercongruences involving products of two binomial coefficients modulo p⁴

2022/01/12 by Mao, Guo-Shuai
#Combinatorics (math.CO) #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2201.06951

Abstract

In this paper, we mainly prove a congruence conjecture of Z.-W. Sun \citeSjnt: Let p>5 be a prime. Then ∑_k=(p+1)/2^p-1\frac\binom2kk²k16^k≡-\frac212H_p-1\pmodp⁴, where H_n denotes the n-th harmonic number.

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