Diophantine equations

Includes index

Includes bibliographical references

1. Introduction
2. Equations Proved Impossible by Congruence Considerations
3. Equations Involving Sums of Squares
4. Quartic Equations with Only Trivial Solutions
5. Some Linear Equations
6. Properties of Congruences
7. Homogeneous Equations of the Second Degree
8. Pell's Equation
9. Rational Solutions Derived from Given Ones
10. Rational Points on Some Cubic Curves
11. Rational Points on Cubic Surfaces
12. Rational and Integer Points on Quartic Surfaces
13. Integer Solutions of Some Cubic Equations in Three Variables
14. Simple Algebraic Considerations
15. Applications of Algebraic Number Theory
16. Finite Basis Theorem for the Rational Points on a Cubic Curve f(x, y, z) = 0 of Genus One
17. Rational Points on Curves of Genus g = 0 or 1 and g > 1
18. Representation of Numbers by Homogeneous Forms in Two Variables
19. Representation of Numbers by Special Binary Quadratic and Quaternary Quadratic Forms
20. Representation of Numbers by Homogeneous Forms in Several Variables
21. Representation of Numbers by Polynomials
22. Thue's Theorem on the Integer Solutions of f(x, y) = m
23. Local Methods of p-adic Applications
24. Binary Cubic Forms
25. Binary Quartic Forms
26. The Equation y² = x³ + k
27. The Equation y² = ax³ + bx² + cx + d
28. Some Equations of Degree > 3
29. Fermat's Last Theorem
30. Miscellaneous Results