A Course in Number Theory

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Clarendon Press, 1995 - Mathematics - 398 pages
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This textbook covers the main topics in number theory as taught in universities throughout the world. Number theory deals mainly with properties of integers and rational numbers; it is not an organized theory in the usual sense but a vast collection of individual topics and results, with some coherent sub-theories and a long list of unsolved problems. This book excludes topics relying heavily on complex analysis and advanced algebraic number theory. The increased use of computers in number theory is reflected in many sections (with much greater emphasis in this edition). Some results of a more advanced nature are also given, including the Gelfond-Schneider theorem, the prime number theorem, and the Mordell-Weil theorem. The latest work on Fermat's last theorem is also briefly discussed. Each chapter ends with a collection of problems; hints or sketch solutions are given at the end of the book, together with various useful tables.
 

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Contents

DIVISIBILITY
1
MULTIPLICATIVE FUNCTIONS
17
CONGRUENCE THEORY
32
QUADRATIC RESIDUES
58
ALGEBRAIC TOPICS
80
SUMS OF SQUARES AND GAUSS SUMS
102
CONTINUED FRACTIONS
124
TRANSCENDENTAL NUMBERS
146
PARTITIONS
210
THE PRIME NUMBERS
226
TWO MAJOR THEOREMS ON THE PRIMES
247
DIOPHANTINE EQUATIONS
273
BASIC THEORY
293
FURTHER RESULTS
317
ANSWERS AND HINTS TO PROBLEMS
347
BIBLIOGRAPHY
389

QUADRATIC FORMS
164
GENERA AND THE CLASS GROUP
186

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About the author (1995)

H. E. Rose is at University of Bristol.

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