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

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Showing 2015Show all

6 papers · 1 filter

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

A Stern-type congruence for the Schroder numbers

Hui-Qin Cao, Hao Pan

For the Schröder number $S_{n} = k = 0 \sum n (k n) (k n + k) \frac{1}{k + 1},$ we prove that $S_{n + 2^{α}} \equiv S_{n} + 2^{α + 1} (mod 2^{α + 2}),$ where $n \geq 1$ and $α \geq 1$ .

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.CO2015

A Lucas-type congruence for q-Delannoy numbers

Hao Pan

We prove a Lucas-type congruence for q-Delannoy numbers.

math.NT2015★ 2 cited

The Rodriguez-Villegas type congruences for truncated q-hypergeometric functions

Victor J. W. Guo, Hao Pan, Yong Zhang

We prove some Rodriguez-Villegas type congruences for truncated q-hypergeometric functions.

math.CO2015

Note on polynomial recurrence

Hao Pan

Let $(X, μ, T_{1}, ..., T_{l})$ be a measure-preserving system with those $T_{i}$ are commuting. Suppose that the polynomials $p_{1} (t), ..., p_{l} (t) \in Z [t]$ with $p_{j} (0) = 0$ have distinct degr…