Part 1. Diophantine Equations
Chapter 1. Elementary Methods for Solving Diophantine Equations
1.1. The Decomposition Method
1.2. Solving Diophantine Equations Using Inequalities
1.3. The Parametric Method
1.4. The Modular Arithmetic Method
1.5. The Method of Mathematical Induction
1.6 .Fermat's Method of Infinite Descent (FMID)
1.7. Miscellaneous Diophantine Equations
Chapter 2. Some Classical Diophantine Equations
2.1. Linear Diophantine Equations
2.2. Pythagorean Triples and Related Problems
2.3. Other Remarkable Equations
Chapter 3. Pell's-Type Equations
3.1. Pell's Equation: History and Motivation
3.2. Solving Pell's Equation by Elementary Methods
3.3. The Equation ax2-by2=1
3.4. The Negative Pell's Equation
Part 2. Solutions to Exercises and Problems
Chapter 1. Elementary Methods for Solving Diophantine Equations
1.1. The Decomposition Method
1.2. Solving Diophantine Equations Using Inequalities
1.3. The Parametric Method
1.4. The Modular Arithmetic Method
1.5. The Method of Mathematical Induction
1.6 .Fermat's Method of Infinite Descent (FMID)
1.7. Miscellaneous Diophantine Equations
Chapter 2. Some Classical Diophantine Equations
2.1. Linear Diophantine Equations
2.2. Pythagorean Triples and Related Problems
2.3. Other Remarkable Equations
Chapter 3. Pell's-Type Equations
3.1. Pell's Equation: History and Motivation
3.2. Solving Pell's Equation by Elementary Methods
3.3. The Equation ax2-by2=1
3.4. The Negative Pell's Equation
Bibliography
Index
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