Article
Licensed
Unlicensed
Requires Authentication
Primitive Prime Divisors in Zero Orbits of Polynomials
-
Kevin Doerksen
and
Anna Haensch
Published/Copyright:
May 31, 2012
Abstract.
Let 
be a sequence of integers. A primitive prime divisor of a term 
is a prime which divides but does not divide any of the previous terms of the sequence. A zero orbit of a polynomial 
is a sequence of integers 
where the n-th term is the n-th iterate of 
at 0. We consider primitive prime divisors of zero orbits of polynomials. In this note, we show that for 
in 
, where 
and 
, every iterate in the zero orbit of 
contains a primitive prime divisor whenever zero has an infinite orbit. If 
, then every iterate after the first contains a primitive prime divisor.
Keywords: Arithmetic Dynamics; Polynomial Maps; Orbits; Primitive Prime Divisors; Rigid Divisibility Sequences
Received: 2010-09-20
Revised: 2011-06-02
Accepted: 2012-01-01
Published Online: 2012-05-31
Published in Print: 2012-June
© 2012 by Walter de Gruyter Berlin Boston
You are currently not able to access this content.
You are currently not able to access this content.
Articles in the same Issue
- Masthead
- On a Theorem of Prachar Involving Prime Powers
- A Novel Approach to the Discovery of Binary BBP-Type Formulas for Polylogarithm Constants
- A Recurrence Related to the Bell Numbers
- Sum-Product Estimates Applied to Waring's Problem over Finite Fields
- Communal Partitions of Integers
- On Computation of Exact van der Waerden Numbers
- On the Complexity of Chooser–Picker Positional Games
- Partition of an Integer into Distinct Bounded Parts, Identities and Bounds
- A Correlation Identity for Stern's Sequence
- Primitive Prime Divisors in Zero Orbits of Polynomials
Keywords for this article
Arithmetic Dynamics;
Polynomial Maps;
Orbits;
Primitive Prime Divisors;
Rigid Divisibility Sequences
Articles in the same Issue
- Masthead
- On a Theorem of Prachar Involving Prime Powers
- A Novel Approach to the Discovery of Binary BBP-Type Formulas for Polylogarithm Constants
- A Recurrence Related to the Bell Numbers
- Sum-Product Estimates Applied to Waring's Problem over Finite Fields
- Communal Partitions of Integers
- On Computation of Exact van der Waerden Numbers
- On the Complexity of Chooser–Picker Positional Games
- Partition of an Integer into Distinct Bounded Parts, Identities and Bounds
- A Correlation Identity for Stern's Sequence
- Primitive Prime Divisors in Zero Orbits of Polynomials
