Primitive Prime Divisors in Polynomial Arithmetic Dynamics
Brian Rice · Zenodo (CERN European Organization for Nuclear Research) · 2007
The question of which terms of a recurrence sequence fail to have primitive prime divisors has been significantly studied for several classes of linear recurrence sequences and for elliptic divisibility sequences. In this paper, we consider the question for sequences generated by the iteration of a polynomial. For two classes of polynomials f(x) ∈ Z[x] and initial values a1 ∈ Z, we show that the sequence (an) given by an+1 = f(an) for n ≥ 1 has only finitely many terms which have no primitive prime divisor.