Supercongruences for Apéry-like numbers

Abstract

AbstractIt is known that the numbers which occur in Apéryʼs proof of the irrationality of ζ(2) have many interesting congruence properties while the associated generating function satisfies a second order differential equation. We prove supercongruences for a generalization of numbers which arise in Beukersʼ and Zagierʼs study of integral solutions of Apéry-like differential equations