Beschreibung
This problem-solving book is an introduction to the study of Diophantine equations, a class of equations in which only integer solutions are allowed. The presentation features some classical Diophantine equations, including linear, Pythagorean, and some higher degree equations, as well as exponential Diophantine equations. Many of the selected exercises and problems are original or are presented with original solutions. An Introduction to Diophantine Equations: A Problem-Based Approach is intended for undergraduates, advanced high school students and teachers, mathematical contest participants including Olympiad and Putnam competitors as well as readers interested in essential mathematics. The work uniquely presents unconventional and non-routine examples, ideas, and techniques.
Inhaltsverzeichnis
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.-Fermat¿s Method of Infinite Descent (FMID).-Miscellaneous Diophantine Equations.-Some Classical Diophantine Equation.-Linear Diophantine Equation.-Pythagorean Triples and Related Problems.-Other Remarkable Equations.-Pell¿s-Type Equations.-Pell¿s Equation: History and Motivation.-Solving Pell¿s Equation by Elementary Methods.-The Equation ax^2-by^2=1.-The Negative Pell¿s 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.-Fermat¿s Method of Infinite Descent (FMID).-Miscellaneous Diophantine Equations.-Some Classical Diophantine Equation.-Linear Diophantine Equation.-Pythagorean Triples and Related Problems.-Other Remarkable Equations.-Pell¿s-Type Equations.-Solving Pell¿s Equation by Elementary Methods.-The Equation ax^2-by^2=1.-The Negative Pell¿s Equation.-References.-Index.
