Zhi-Hong Sun

collaborators

2 papers

math.NT2024

Congruences for the Apéry numbers modulo $p^{3}$

Zhi-Hong Sun

Let ${A_{n}^{'}}$ be the Apéry numbers given by $A_{n}^{'} = \sum_{k = 0}^{n} (k n)^{2} (k n + k) .$ For any prime $p \equiv 3 (mod 4)$ we show that $A'_{\frac{p-1}2}\equiv \frac{p^2}3\binom{\fr…

math.NT2024

Supercongruences via Beukers' method

Zhi-Hong Sun, Dongxi Ye

Recently, using modular forms F. Beukers posed a unified method that can deal with a large number of supercongruences involving binomial coefficients and Apéry-like numbers. In thi…

Congruences for the Apéry numbers modulo p3

Supercongruences via Beukers' method

Congruences for the Apéry numbers modulo $p^{3}$