# The Z-densities of the Fibonacci Sequence

## Electronic Theses and Dissertations

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- title
- The Z-densities of the Fibonacci Sequence
- author
- Cubre, Paul
- abstract
- Paul S. Bruckman and Peter G. Anderson made a conjecture about the Z-densities of the Fibonacci sequence, F(n), based on computational results. For a prime p, Z(p) is the ``Fibonacci entry-point of n" or the smallest positive integer n such that p divides F(n), M(m,x) is the number of primes p is less than x such that m divides Z(p), and pi(x) is the number of primes less than x. We may define the ``Z-density of m" to be Z(m) is the limit of x to infinity of M(m,x) divided by pi(x). The conjecture gives a formula for Z(m) for all positive m. We will prove the conjecture of Bruckman and Anderson.
- subject
- Arithmetic Dynamics
- Fibonacci
- Z-Densities
- contributor
- Rouse, Jeremy A (committee chair)
- Howard, Fred T (committee member)
- date
- 2012-06-12T08:36:06Z (accessioned)
- 2012-06-12T08:36:06Z (available)
- 2012 (issued)
- degree
- Mathematics (discipline)
- identifier
- http://hdl.handle.net/10339/37313 (uri)
- language
- en (iso)
- publisher
- Wake Forest University
- type
- Thesis

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