The Congruence Question Of Recurrence Sequence Module P

In this paper, we consider the congruence problem bwtween the terms in any two-degree integer coefficient recurrence sequence. Precisely, we consider the recurrence se-quences satisfying un+2=aun+i+bun, where a, b, u1, u2 are given integers. We show that, there exists a set consisting of finite number of prime S such that if p is not in S, then un+p2-1= un(mod p) for every positive integral number n; furthermore, there exists a positive integer N such that, if p is not in S and N|p - 1, then then un+p-1= unmod p.Finally we extend our result on two-degree recurrence sequence to the general case of high-degree recurrence sequences, obtaining a similar but less precise result.