An Introduction to Diophantine Equations

Editora:

Springer Nature B.V.

Código:

491_9780817645489

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Preface.-Part 1: Diophantine Equations.-Elementary Methods for Solving Diophantine Equations.-The Decomposition Method.-Solving Diophantine Equations Using Inequalities.-The Parametric Method.-The Modular Arithmetic Method.-The Method of Mathematical Induction.-Fermats Method of Infinite Descent (FMID).-Miscellaneous Diophantine Equations.-Some Classical Diophantine Equation.-Linear Diophantine Equation.-Pythagorean Triples and Related Problems.-Other Remarkable Equations.-Pells-Type Equations.-Pells Equation: History and Motivation.-Solving Pells Equation by Elementary Methods.-The Equation ax^2-by^2=1.-The Negative Pells Equation.-Part 2: Solutions to Exercises and Problems.-Elementary Methods for Solving Diophantine Equations.-The Decomposition Method.-Solving Diophantine Equations Using Inequalities.-The Parametric Method.-The Modular Arithmetic Method.-The Method of Mathematical Induction.-Fermats Method of Infinite Descent (FMID).-Miscellaneous Diophantine Equations.-Some Classical Diophantine Equation.-Linear Diophantine Equation.-Pythagorean Triples and Related Problems.-Other Remarkable Equations.-Pells-Type Equations.-Solving Pells Equation by Elementary Methods.-The Equation ax^2-by^2=1.-The Negative Pells Equation.-References.-Index.

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