Primitive prime divisors in backward orbits

摘要

Let f be a polynomial, a, b be two algebraic numbers, and (an)n >= 1 be a sequence satisfying f (a1) = a and f (an) = an-1 for all n >= 2. We generalize the concept of primitive prime divisors to the shifted sequence (an - b)n >= 1 and study the generalized Zsigmondy set, that is, the set of n such that all prime ideal divisors of an - b divide at least one prior term. The finiteness of Zsigmondy sets are determined in various cases.

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