Resumen de Diviseurs premiers de suites recurrentes no lineaires

Jean Paul Bézivin

• Let $P$ be a polynomial with rational integer coefficients, and $u(n), n\in\mathbb{N}$, a linear recurrent sequence of rational integers. Define a sequence $a(n)$ of rational integers by its first term and the (non-linear in general) recurrence formula $a(n+1)=P(a(n))+u(n)$.\newline We say that the non zero rational integer $m$ is a divisor of the sequence $a(n)$ if $m$ divides some non-zero term of the sequence.\newline In this paper, we characterize the sequences $a(n)$ with only a finite number of prime divisors.