An Introduction to Diophantine Equations

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.