Pell's Equation

2003. Auflage 2003
ISBN: 978-0-387-95529-2
Verlag: Springer

Buch, Englisch, 212 Seiten, Format (B × H): 164 mm x 244 mm, Gewicht: 469 g

Reihe: Problem Books in Mathematics

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.

Zielgruppe

Research

Autoren/Hrsg.

Barbeau, Edward J

Fachgebiete

• Mathematik | Informatik Mathematik Mathematik Allgemein Populäre Darstellungen der Mathematik
• Mathematik | Informatik Mathematik Mathematik Allgemein Diskrete Mathematik, Kombinatorik
• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen
• Mathematik | Informatik Mathematik Algebra Zahlentheorie

Inhaltsverzeichnis

The Square Root of 2.- Problems Leading to Pel?s Equation and Preliminary Investigations.- Quadratic Surds.- The Fundamental Solution.- Tracking Down the Fundamental Solution.- Pel?s Equation and Pythagorean Triples.- The Cubic Analogue of Pel?s Equation.- Analogues of the Fourth and Higher Degrees.- A Finite Version of Pel?s Equation.