An Introduction to Diophantine Equations

✍ Scribed by Titu Andreescu, Dorin Andrica

• Tongue: English
• Leaves: 205
• Category: Library

✦ Table of Contents

Contents......Page 8
Preface......Page 10
Part 1. Diophantine Equations......Page 14
1.1. The Decomposition Method......Page 16
1.2. Solving Diophantine Equations Using Inequalities......Page 22
1.3. The Parametric Method......Page 27
1.4. The Modular Arithmetic Method......Page 34
1.5. The Method of Mathematical Induction......Page 39
1.6. Fermat's Method of Infinite Descent (FMID)......Page 49
1.7. Miscellaneous Diophantine Equations......Page 59
2.1. Linear Diophantine Equations......Page 66
2.2. Pythagorean Triples and Related Problems......Page 74
2.3. Other Remarkable Equations......Page 84
3.1. Pell's Equation: History and Motivation......Page 110
3.2. Solving Pell's Equation by Elementary Methods......Page 113
3.3. The Equation ax^2-by^2 = 1......Page 121
3.4. The Negative Pell's Equation......Page 124
Part 2. Solutions to Exercises and Problems......Page 128
1.1. The Decomposition Method......Page 130
1.2. Solving Diophantine Equations Using Inequalities......Page 135
1.3. The Parametric Method......Page 140
1.4. The Modular Arithmetic Method......Page 143
1.5. The Method of Mathematical Induction......Page 149
1.6. Fermat's Method of Infinite Descent (FMID)......Page 156
1.7. Miscellaneous Diophantine Equations......Page 167
2.1. Linear Diophantine Equations......Page 176
2.2. Pythagorean Triples and Related Problems......Page 181
2.3. Other Remarkable Equations......Page 183
3.2. Solving Pell's Equation by Elementary Methods......Page 190
3.3. The Equation ax^2-by^2 = 1......Page 192
3.4. The Negative Pell's Equation......Page 194
Bibliography......Page 198
Index......Page 202