Date of Award
6-2008
Document Type
Union College Only
Degree Name
Bachelor of Science
Department
Mathematics
First Advisor
Paul Friedman
Language
English
Keywords
plane, define, gaussian, infinity, number
Abstract
The following popular question from number theory motivated this paper: ”Can someone with finite step size walk to infinity while restricting his or her possible steps to prime numbers?” We will show the answer to be ”No,” before expanding the problem. If instead of looking at the real number line we look at the complex plane, the problem becomes much harder. First, we must define the ”Gaussian integers” of this plane and then define what makes a Gaussian integer prime. Next, we will prove that by limiting the walker’s range of motion to sectors of the plane, the walker can never reach infinity. We will also show that the union of these sectors is arbitrarily close to the entire plane.
Recommended Citation
Cohen, Steve, "A study of Gaussian integers" (2008). Honors Theses. 1518.
https://digitalworks.union.edu/theses/1518