This textbook deals with the central topics in number theory as taught in universities throughout the world. Number theory is not an organized theory in the usual sense but a vast collection of individual topics and results, with some coherent subtheories and a long list of unsolved problems. Excluding topics which rely heavily on more advanced complex analysis and algebraic number theory this book considers eight central areas: divisibility and multiplicative functions; congruences and quadratic residues; an introduction to algebraic numbers and sums of squares; continued fractions, diophantine approximation and transducence; quadratic forms; partitions; the prime numbers; diophantine equations and elliptic curves. Some more advanced results are also given including the Gelfond-Schneider theorem, the prime number theorem and the Mordell-Weil theorem. Each chapter ends with a collection of problems; hints or sketch solutions are given at the back of the book together with various tables.
- ISBN10 019853261X
- ISBN13 9780198532613
- Publish Date 12 May 1988 (first published 5 May 1988)
- Publish Status Out of Print
- Out of Print 2 June 2000
- Publish Country GB
- Publisher Oxford University Press
- Imprint Clarendon Press
- Format Paperback
- Pages 364
- Language English