Super congruences concerning binomial coefficients and Apéry-like numbers

Abstract

Let p be a prime with p > 3, and let a, b be two rational p−integers. In this paper we present general congruences forFor n = 0, 1, 2, . . . let D n and b n be Domb and Almkvist-Zudilin numbers, respectively. We also establish congruences forin terms of certain binary quadratic forms.

A $p$-adic analogue of Chan and Verrill's formula for $1/π$

“…We remark that congruence properties for the Almkvist-Zudilin numbers have been widely investigated by Amdeberhan and Tauraso [2], Chan, Cooper and Sica [4], and Z.-H. Sun [21][22][23].…”