Hao Pan

activity

20042026

most cited

p

-adic analogues of hypergeometric identities

11 citations · 115 across the 90 of their papers we have counts for

collaborators

93 papers

math.NT2026

An ergodic approach to equations of the form $x + y = ⌊ α (n)⌋$

Vitaly Bergelson, Hao Pan, Saúl Rodríguez Martín

Motivated by questions and results of Erdős, Sárközy and Sós (1989), and Khalfalah and Szemerédi (2006), we introduce an ergodic approach to additive problems concerning solutions…

math.NT2022

Partitions of nonnegative integers with identical representation functions

Cui-Fang Sun, Hao Pan

Let $N$ be the set of all nonnegative integers. For any integer $r$ and $m$ , let $r + m N = {r + mk : k \in N}$ . For $S \subseteq N$ and $n\in \mathbb{N}…

math.NT2022

Partitions of finite nonnegative integer sets with identical representation functions

Cui-Fang Sun, Hao Pan

Let $N$ be the set of all nonnegative integers. For $S \subseteq N$ and $n \in N$ , let the representation function $R_{S} (n)$ denote the number of solution…

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

A new theorem on quadratic residues modulo primes

Qing-Hu Hou, Hao Pan, Zhi-Wei Sun

Let $p > 3$ be a prime, and let $(\frac{\cdot}{p})$ be the Legendre symbol. Let $b \in Z$ and $ε \in {\pm 1}$ . We mainly prove that $$\left|\left\{N_p(a,b):\ 1<a<p\ \te…

math.NT2020★ 2 cited

Supercongruences for central trinomial coefficients

Hao Pan, Zhi-Wei Sun

For each $n = 0, 1, 2, \dots$ , the central trinomial coefficient $T_{n}$ is the coefficient of $x^{n}$ in the expansion of $(x^{2} + x + 1)^{n}$ . Let $p > 3$ be a prime, and let $n$ be any positive…