# Greatest common divisors of iterates of polynomials

Liang-Chung Hsia, Thomas J. Tucker

1 引文 (Scopus)

### 摘要

Following work of Bugeaud, Corvaja, and Zannier for integers, Ailon and Rudnick prove that for any multiplicatively independent polynomials, a,bεℂℂ[x], there is a polynomial h such that for all n, we have gcd(an-1,bn-1)|h We prove a compositional analog of this theorem, namely that if f,gεℂℂ[x] are compositionally independent polynomials and c(x)εℂℂ[x], then there are at most finitely many λ with the property that there is an n such that (x-λ) divides gcd(fon(x)-c(x),gon(x)-c(x)).

原文 英語 1437-1459 23 Algebra and Number Theory 11 6 https://doi.org/10.2140/ant.2017.11.1437 已發佈 - 2017 一月 1

### 指紋

Highest common factor
Iterate
Polynomial
Divides
Analogue
Integer
Theorem

### ASJC Scopus subject areas

• Algebra and Number Theory

### 引用此文

Greatest common divisors of iterates of polynomials. / Hsia, Liang-Chung; Tucker, Thomas J.

Hsia, Liang-Chung ; Tucker, Thomas J. / Greatest common divisors of iterates of polynomials. 於: Algebra and Number Theory. 2017 ; 卷 11, 編號 6. 頁 1437-1459.
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