Quadratic Diophantine Equations [electronic resource] / by Titu Andreescu, Dorin Andrica.
Contributor(s): Andrica, Dorin [author.] | SpringerLink (Online service)Material type: TextSeries: Developments in Mathematics: 40Publisher: New York, NY : Springer New York : Imprint: Springer, 2015Description: XVIII, 211 p. online resourceContent type: text Media type: computer Carrier type: online resourceISBN: 9780387541099Subject(s): Mathematics | Algebra | Number theory | Mathematics | Number Theory | AlgebraAdditional physical formats: Printed edition:: No titleDDC classification: 512.7 LOC classification: QA241-247.5Online resources: Click here to access online
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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.
This monograph 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. The authors motivate the study of quadratic Diophantine equations with excellent examples, open problems, and applications. Moreover, the exposition aptly demonstrates many applications of results and techniques from the study of Pell-type equations to other problems in number theory. 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.