Diviseurs Premiers De Suites Recurrentes Lineaires

Abstract

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 ∈ ℕ, with characteristic polynomial P , there is a positive integer n such that U ( n )≡ 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 .