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Set of prime divisors of a_{n+1}=f(a_n), f polynomial.

Source: Tuymaada 2003, day 2, problem 4.

May 5, 2007
algebrapolynomialcalculusintegrationnumber theory proposednumber theory

Problem Statement

Given are polynomial f(x)f(x) with non-negative integral coefficients and positive integer a.a. The sequence {an}\{a_{n}\} is defined by a1=a,a_{1}=a, an+1=f(an).a_{n+1}=f(a_{n}). It is known that the set of primes dividing at least one of the terms of this sequence is finite. Prove that f(x)=cxkf(x)=cx^{k} for some non-negative integral cc and k.k.
Proposed by F. Petrov
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