Congruences and telescopings of P-recursive sequences

Abstract

A P-recursive sequence is a sequence which satisfies a linear recurrence relation with polynomial coefficients. For a P-recursive sequence and its power , we give a method to construct a polynomial so that the sum of equals a finite sum of the products of a polynomial and , where are integers. When these summands have a common factor , we will derive that is a factor of the sum . This method can be used to derive some congruences. We give some examples to exhibit the applications of the method.