This paper seeks to explain in the simplest terms possible a paper written by Umberto Zannier. Though Zannier says that his is "a simple elementary method," there are still steps in his paper that are quite subtle. The tools needed to follow his proof are in the hands of most Algebra students, though which tools to use and how to use them may not be obvious. This essay hopes to make the path from conception to conclusion as clear and easy as possible, with simple proofs and examples to show the way.

Author Bio

I am a senior mathematics major at Washington University in St. Louis. This paper was writtenas part of a senior honors project. I plan to graduate with honors in May and attend graduateschool in mathematics this fall. My hobbies include reading and most sports, such as golf,tennis, and running. Soccer is more than a hobby; highlights include playing for the WashingtonUniversity Men's Varsity and the New College 1st XI (Oxford). Most summers I can be foundmolding young soccer players as a coach/counselor at WashU soccer camps.