Date of Award

4-17-2006

Document Type

Thesis

Degree Name

Bachelor of Arts

Department

Mathematics

First Advisor

Dr. Gary R. Greenfield

Abstract

This thesis considers a variation of the 3x+1, or Collatz, Problem involving a function we call the Conway function. The Conway function is defined by letting C3(n)=2k for n=3k and C3(n)=4k±1 for n=3k±1, where n is an integer. The iterates of this function generate a few 'short' cycles, but the s' tructural dynamics are otherwise unknown. We investigate properties of the Conway function and other related functions. We also discuss the possibility of using the Conway function to generate keys for cryptographic use based on a fast, efficient binary implemenation of the function. Questions related to the conjectured tree-like structure of the 3x+1 Problem and to other decidable tree-like structures are also considered.

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