Quadratic Diophantine Equations. Springer Monographs in Mathematics

Seitenzahl:

250

Erschienen bei:

Springer

Beschreibung

This text treats the classical theory of quadratic diophantine equations and guides the reader through the last two decades of computational techniques and progress in the area. These new techniques combined with the latest increases in computational power shed new light on important open problems.
Key features:
Motivates the study of quadratic diophantine equations with excellent examples and open problems
Examines Pell’s equation and its generalizations
Presents important quadratic diophantine equations and applications
Computational techniques solve classical and outstanding problems
The book is intended for advanced undergraduate and graduate students as well as researchers. It challenges the reader to apply not only specific techniques and strategies, but also to employ methods and tools from other areas of mathematics, such as algebra and analysis.

Kurzbeschreibung

This text treats the classical theory of quadratic diophantine equations and guides the reader through the last two decades of computational techniques and progress in the area. These new techniques combined with the latest increases in computational power shed new light on important open problems.
Key features:
Motivates the study of quadratic diophantine equations with excellent examples and open problems
Examines Pell's equation and its generalizations
Presents important quadratic diophantine equations and applications
Computational techniques solve classical and outstanding problems
The book is intended for advanced undergraduate and graduate students as well as researchers. It challenges the reader to apply not only specific techniques and strategies, but also to employ methods and tools from other areas of mathematics, such as algebra and analysis. TOC:Introduction.-Why Pell's equation?.-Two useful techniques: continued fractions and quadratic rings.-Pell's equation.-General Pell's equation.-Equations reducible to Pell's equation.-Diophantine representations of some sequences.-Other applications.-Glossary.-References.-Index.

Mehr über...

Mehr über:  Algebra, algebra, Zahlentheorie, number theory, diophantine equations, Pell's equation

Mehr von: 

Mehr von:  Titu Andreescu, Dorin Andrica, Springer