Guo-Shuai Mao

activity

20142023

most citedNew congruences involving products of two binomial coefficients

16 citations · 88 across the 24 of their papers we have counts for

collaborators

24 papers

math.NT2023

Proof of two congruence conjectures of Z.-W. Sun

Guo-Shuai Mao

In this paper, we mainly prove two congruence conjecture of Z.-W. Sun. Let $p \equiv 3 (mod 4)$ be a prime. Then $$\sum_{k=0}^{p-1}\frac{\binom{2k}k^2}{8^k}\equiv-\sum_{k=0}^{p-1}\fra…

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.NT2022

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

Guo-Shuai Mao

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_{…

math.NT2021

Supercongruences involving Domb numbers and binary quadratic forms

Guo-Shuai Mao, Michael J. Schlosser

In this paper, we prove two recently conjectured supercongruences (modulo $p^{3}$ , where $p$ is any prime greater than $3$ ) of Zhi-Hong Sun on truncated sums involving the Domb numbe…

math.NT2021★ 2 cited

Proof of some conjectural congruences involving Domb numbers

Guo-Shuai Mao, Yan Liu

In this paper, we mainly prove the following conjectures of Z.-H. Sun \cite{SH2}: Let $p > 3$ be a prime. If $p \equiv 1 (mod 3)$ and $p = x^{2} + 3 y^{2}$ , then we have $$ \sum_{k=0}^{p-1}\frac{…

math.NT2021

On two congruence conjectures of Z.-W. Sun involving Franel numbers

Guo-Shuai Mao, Yan Liu

In this paper, we mainly prove the following conjectures of Z.-W. Sun \cite{S13}: Let $p > 2$ be a prime. If $p = x^{2} + 3 y^{2}$ with $x, y \in Z$ and $x \equiv 1 (mod 3)$ , then $$x\equi…

math.NT2021★ 1 cited

Proof of some congruence conjectures of Z.-H. Sun involving Apéry-like numbers

Guo-Shuai Mao

In this paper, we mainly prove the following conjecture of Z.-H. Sun cite{SH20}: Let $p > 3$ be a prime. Then $$\sum_{k=0}^{p-1}\binom{2k}k\frac{3k+1}{(-16)^k}f_k\equiv(-1)^{(p-1)/2}…

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★ 2 cited

On a supercongruence conjecture of Z.-W. Sun

Guo-Shuai Mao

In this paper, we partly prove a supercongruence conjectured by Z.-W. Sun in 2013. Let $p$ be an odd prime and let $a \in Z^{+}$ . Then if $p \equiv 1 (mod 3)$ , we have \begin{al…

math.NT2020★ 6 cited

Proof of a conjecture of Adamchuk

Guo-Shuai Mao

In this paper, we prove a congruence which confirms a conjecture of Adamchuk. For any prime $p \equiv 1 (mod 3)$ and $a \in Z^{+}$ , we have \begin{align*} \sum_{k=1}^{\frac{2}3(…

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…

math.NT2020★ 8 cited

On two congruences involving Apéry and Franel numbers

Guo-Shuai Mao

In this paper, we generalise a congruence which proved by V. J.-W. Guo and J. Zeng \cite{gz-jnt-2012} involving Apéry numbers, and we obtain a congruence involving Franel numbers w…

math.NT2019★ 3 cited

Proof of two supercongruences by the Wilf-Zeilberger method

Guo-Shuai Mao

In this paper, we prove two supercongruences by the Wilf-Zeilberger method. One of them is, for any prime $p > 3$ , \begin{align*} \sum_{n=0}^{(p-1)/2}\frac{3n+1}{(-8)^n}\binom{2n}n^3…

math.NT2019★ 3 cited

Proof of two supercongruences conjectured by Z.-W. Sun

Guo-Shuai Mao, Chen-Wei Wen

In this paper, we prove two supercongruences conjectured by Z.-W. Sun via the Wilf-Zeilberger method. One of them is, for any prime $p > 3$ , \begin{align*} \sum_{n=0}^{p-1}\frac{6n+1…

math.NT2019★ 2 cited

Proof of some supercongruences via the Wilf-Zeilberger method

Guo-Shuai Mao

In this paper, we prove some supercongruences via the Wilf-Zeilberger method. For instance, for any odd prime $p$ and positive integer $r$ and $δ \in {1, 2}$ , we have \begin{align*}…

math.NT2018★ 2 cited

On the divisibility of some truncated hypergeometric series

Guo-Shuai Mao, Hao Pan

Let $p$ be an odd prime and $r \geq 1$ . Suppose that $α$ is a $p$ -adic integer with $α \equiv 2 a (mod p)$ for some $1 \leq a < (p + r) / (2 r + 1)$ . We confirm a conjecture of Sun and prove that…

math.NT2017★ 11 cited

$p$ -adic analogues of hypergeometric identities

Guo-Shuai Mao, Hao Pan

We prove some supercongruences for the truncated hypergeometric series.

math.NT2016★ 16 cited

New congruences involving products of two binomial coefficients

Guo-Shuai Mao, Zhi-Wei Sun

Let $p > 3$ be a prime and let $a$ be a positive integer. We show that if $p \equiv 1 (mod 4)$ or $a > 1$ then $$\sum_{k=0}^{\lfloor\frac34p^a\rfloor}\frac{\binom{2k}k^2}{16^k}\equivł(\fr…

math.NT2015

Proof of a conjecture involving Sun polynomials

Victor J. W. Guo, Guo-Shuai Mao, Hao Pan

The Sun polynomials $g_{n} (x)$ are defined by \begin{align*} g_n(x)=\sum_{k=0}^n{n\choose k}^2{2k\choose k}x^k. \end{align*} We prove that, for any positive integer $n$ , there hold \…

math.NT2015★ 13 cited

Proof of two supercongruences conjectured by Z.-W.Sun involving Catalan-Larcombe-French numbers

Guo-Shuai Mao

The harmonic numbers $H_n=\sum_{0<k\ls n}1/k\ (n=0,1,2,\ldots)$ play important roles in mathematics. With helps of some combinatorial identities, we establish the following two con…

math.NT2015★ 6 cited

Supercongruences on some binomial sums involving Lucas sequences

Guo-Shuai Mao, Hao Pan

In this paper, we confirm several conjectured congruences of Sun concerning the divisibility of binomial sums. For example, with help of a quadratic hypergeometric transformation,…

math.NT2015

Proof of some congruence conjectures of Guo and Liu

Guo-Shuai Mao

Let $n$ and $r$ be positive integers. Define the numbers $S_{n}^{(r)}$ by $S_{n}^{(r)} = \sum_{k = 0}^{n} (k n)^{2} (k 2 k) (2 k + 1)^{r} .$ In this paper we prove some conjectures of Guo…

math.NT2015★ 9 cited

Proof of Sun's conjectures on super congruences and the divisibility of certain binomial sums

Guo-Shuai Mao, Tao Zhang

In this paper, we prove two conjectures of Z.-W. Sun: $$2n\binom{2n}n\big|\sum_{k=0}^{n-1}(3k+1)\binom{2k}k^3{16}^{n-1-k}\ \mbox{for}\ \mbox{all}\ n=2,3,\cdots,$$ and $$\sum_{k=0}^…

math.NT2014★ 3 cited

Two congruences involving harmonic numbers with applications

Guo-Shuai Mao, Zhi-Wei Sun

The harmonic numbers $H_{n} = \sum_{0 < k \leq n} 1/ k (n = 0, 1, 2, \dots)$ play important roles in mathematics. Let $p > 3$ be a prime. With helps of some combinatorial identities, we establish…

Proof of two congruence conjectures of Z.-W. Sun

On the supercongruences involving harmonic numbers of order 2

Supercongruences involving products of two binomial coefficients modulo p4

Supercongruences involving Domb numbers and binary quadratic forms

Proof of some conjectural congruences involving Domb numbers

On two congruence conjectures of Z.-W. Sun involving Franel numbers

Proof of some congruence conjectures of Z.-H. Sun involving Apéry-like numbers

Proof of a conjectural supercongruence modulo p5

On a supercongruence conjecture of Z.-W. Sun

Proof of a conjecture of Adamchuk

Three pairs of congruences concerning sums of central binomial coefficients

On two congruences involving Apéry and Franel numbers

Proof of two supercongruences by the Wilf-Zeilberger method

Proof of two supercongruences conjectured by Z.-W. Sun

Proof of some supercongruences via the Wilf-Zeilberger method

On the divisibility of some truncated hypergeometric series

p-adic analogues of hypergeometric identities

New congruences involving products of two binomial coefficients

Proof of a conjecture involving Sun polynomials

Proof of two supercongruences conjectured by Z.-W.Sun involving Catalan-Larcombe-French numbers

Supercongruences on some binomial sums involving Lucas sequences

Proof of some congruence conjectures of Guo and Liu

Proof of Sun's conjectures on super congruences and the divisibility of certain binomial sums

Two congruences involving harmonic numbers with applications

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

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

$p$ -adic analogues of hypergeometric identities