Guo-Shuai Mao

activity

20202022

most citedOn the supercongruences involving harmonic numbers of order 2

1 citations · 1 across the 2 of their papers we have counts for

collaborators

3 papers

math.NT2022★ 1 cited

On the supercongruences involving harmonic numbers of order 2

Guo-Shuai Mao, Hao Pan

We prove several supercongruences involving the harmonic number of order two $H_{n}^{(2)} := \sum_{k = 1}^{n} 1/ k^{2}$ . For example, if $p > 5$ is prime and $α$ is $p$ -integral, then we can com…

math.NT2021

Proof of a conjectural supercongruence modulo $p^{5}$

Guo-Shuai Mao, Zhi-Wei Sun

In this paper we prove the supercongruence $n = 0 \sum (p - 1) /2 \frac{6 n + 1}{25 6 ^{n}} (n 2 n)^{3} \equiv p (- 1)^{(p - 1) /2} + (- 1)^{(p - 1) /2} \frac{7}{24} p^{4} B_{p - 3} (mod p^{5})$ for any prim…

math.NT2020

Three pairs of congruences concerning sums of central binomial coefficients

Guo-Shuai Mao, Roberto Tauraso

Recently the first author proved a congruence proposed in 2006 by Adamchuk: $\sum_{k = 1}^{⌊ \frac{2 p}{3} ⌋} (k 2 k) \equiv 0 (mod p^{2})$ for any prime $p = 1 (mod 3)$ . I…

On the supercongruences involving harmonic numbers of order 2

Proof of a conjectural supercongruence modulo p5

Three pairs of congruences concerning sums of central binomial coefficients

Proof of a conjectural supercongruence modulo $p^{5}$