### Abstract

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(a^{n}-1,b^{n}-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(f^{on}(x)-c(x),g^{on}(x)-c(x)).

Original language | English |
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Pages (from-to) | 1437-1459 |

Number of pages | 23 |

Journal | Algebra and Number Theory |

Volume | 11 |

Issue number | 6 |

DOIs | |

Publication status | Published - 2017 |

### Keywords

- Composition
- Equidstribution
- Gcd
- Heights

### ASJC Scopus subject areas

- Algebra and Number Theory

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## Cite this

Hsia, L. C., & Tucker, T. J. (2017). Greatest common divisors of iterates of polynomials.

*Algebra and Number Theory*,*11*(6), 1437-1459. https://doi.org/10.2140/ant.2017.11.1437