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The Z-densities of the Fibonacci Sequence

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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
Cubre, Paul (author)
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
title
The Z-densities of the Fibonacci Sequence
type
Thesis

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