Robert D Carmichael

Diophantine Analysis Robert D Carmichael

The author's purpose in writing this book has been to supply the reader with a convenient introduction to Diophantine Analysis. The choice of material has been determined by the end in view. No attempt has been made to include all special results, but a large number of them are to be found both in the text and in the exercises. The general theory of quadratic forms has been omitted entirely, since that subject would require a volume in itself. The reader will therefore miss such an elegant theorem as the following: Every positive integer may be represented as the sum of four squares. Some methods of frequent use in the theory of quadratic forms, in particular that of continued fractions, have been left out of consideration even though they have some value for other Diophantine questions. This is done for the sake of unity and brevity. Probablythese omissions will not be regretted, since there are accessible sources through which one can make acquaintance with the parts of the theory excluded.