Diviseurs premiers de suites récurrentes linéaires. (Prime divisors of linear recurrence sequences) (Q1082361)

Let P be a polynomial with rational integer coefficients. In this paper, we study the rational primes p with the following property: For any linear recurrent sequence of rational integers \(U=U_ n\), \(n\in {\mathbb{N}}\), with characteristic polynomial P, there is a positive integer n such that U(n)\(\equiv 0[p]\). We show, when the polynomial P is irreducible modulo p, that there is a procedure to decide when p satisfy this property. The procedure is connected with a cyclic difference set A depending on p and P.