Quadratic Diophantine Equations

This book reveiws the last two decades of computational techniques and progress in the classical theory of quadratic diophantine equations. Presents important quadratic diophantine equations and applications, and includes excellent examples and open problems.

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. The presentation features two basic methods to investigate and motivate the study of quadratic diophantine equations: the theories of continued fractions and quadratic fields. It also discusses Pell's equation and its generalizations, and presents some important quadratic diophantine equations and applications. The inclusion of examples makes this book useful for both research and classroom settings.

Includes both theoretical and computational examples Explores new computational techniques for quadratic diophantine equations Techniques presented will shed light on important open problems Includes supplementary material: sn.pub/extras

Autorentext

Titu Andreescu is an Associate Professor of Mathematics at the University of Texas at Dallas.

Inhalt
Why Quadratic Diophantine Equations?.- Continued Fractions, Diophantine Approximation and Quadratic Rings.- Pell's Equation.- General Pell's Equation.- Equations Reducible to Pell's Type Equations.- Diophantine Representations of Some Sequences.- Other Applications.