Solving Pell's equation with continued fractions
Type of content
UC permalink
Publisher's DOI/URI
Thesis discipline
Degree name
Bachelor of Science
Publisher
University of Canterbury. Mathematics and Statistics
Journal Title
Journal ISSN
Volume Title
Language
Date
2009
Authors
Unger, Jesse
Abstract
In this report we will use continued fractions to solve Fell's equation x² - Dy² = 1 We explore some of the properties of simple continued fractions, discuss the relationship between reduced quadratic irrationals and purely periodic simple continued fractions and then give the solution to Fell's and the negative Pell equation. We close by summarizing the entire process in the PQa algorithm which also shows us how to solve some Pell-like equations.
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Ngā upoko tukutuku/Māori subject headings
ANZSRC fields of research
Fields of Research::49 - Mathematical sciences::4904 - Pure mathematics::490401 - Algebra and number theory
Rights
Copyright Jesse Unger