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# HM-Brow

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Preface

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*ax*^{2}-by^{2}=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*ax*^{2}-by^{2}=1

3.4. The Negative Pell's Equation

Bibliography

Index

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

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

3.4. The Negative Pell's Equation

Bibliography

Index

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