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