Pell's Equation

Edward J. Barbeau

222 pages, parution le 18/02/2003

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Résumé

Pell's equation is part of a central area of algebraic number theory that treats quadratic forms and the structure of the rings of integers in algebraic number fields. It is an ideal topic to lead college students, as well as some talented and motivated high school students, to a better appreciation of the power of mathematical technique. Even at the specific level of quadratic diophantine equations, there are unsolved problems, and the higher degree analogues of Pell's equation, particularly beyond the third, do not appear to have been well studied.

In this focused exercise book, the topic is motivated and developed through sections of exercises which will allow the readers to recreate known theory and provide a focus for their algebraic practice. There are several explorations that encourage the reader to embark on their own research. A high school background in mathematics is all that is needed to get into this book, and teachers and others interested in mathematics who do not have (or have forgotten) a background in advanced mathematics may find that it is a suitable vehicle for keeping up an independent interest in the subject.

Contents

The square root of 2
Problems leading to Pell's equation and preliminary investigations
Quadratic surds
The fundamental solution
Tracking down the fundamental solution
Pell's equation and pythagorean triples
The cubic analogue of Pell's equation
Analogues of the fourth and higher degrees
A finite version of Pell's equation
Answers and solutions

L'auteur - Edward J. Barbeau

University of Toronto, ON, Canada

Caractéristiques techniques

	PAPIER
Éditeur(s)	Springer
Auteur(s)	Edward J. Barbeau
Parution	18/02/2003
Nb. de pages	222
Format	16 x 24
Couverture	Relié
Poids	466g
Intérieur	Noir et Blanc
EAN13	9780387955292
ISBN13	978-0-387-95529-2