Robert D Carmichael

Diophantine Analysis Robert D Carmichael

The author's purpose in writing this book has been to supply the reader witha convenient introduction to Diophantine Analysis. The choice of material hasbeen determined by the end in view. No attempt has been made to include allspecial results, but a large number of them are to be found both in the textand in the exercises. The general theory of quadratic forms has been omittedentirely, since that subject would require a volume in itself. The reader willtherefore miss such an elegant theorem as the following: Every positive integermay be represented as the sum of four squares. Some methods of frequentuse 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 otherDiophantine questions. This is done for the sake of unity and brevity. Probablythese omissions will not be regretted, since there are accessible sources throughwhich one can make acquaintance with the parts of the theory excluded