Topics in Number Theory

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Courier Corporation, Nov 7, 2002 - Mathematics - 496 pages
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Classic two-part work now available in a single volume assumes no prior theoretical knowledge on reader's part and develops the subject fully. Volume I is a suitable first course text for advanced undergraduate and beginning graduate students. Volume II requires a much higher level of mathematical maturity, including a working knowledge of the theory of analytic functions. Contents range from chapters on binary quadratic forms to the Thue-Siegel-Roth Theorem and the Prime Number Theorem. Includes numerous problems and hints for their solutions. 1956 edition. Supplementary Reading. List of Symbols. Index.
 

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Contents

INTRODUCTION
1
THE EUCLIDEAN ALGORITHM AND ITS CONSEQUENCES
14
CONGRUENCES
24
PRIMITIVE ROOTS AND INDICES
48
QUADRATIC RESIDUES
63
NUMBERTHEORETIC FUNCTIONS AND THE DISTRIBUTION OF PRIMES
81
SUMS OF SQUARES
125
PELLS EQUATION AND SOME APPLICATIONS
137
BINARY QUADRATIC FORMS
1
ALGEBRAIC NUMBERS
34
APPLICATIONS TO RATIONAL NUMBER THEORY
82
THE THUESIEGELROTH THEOREM
121
IRRATIONALITY AND TRANSCENDENCE
161
DIRICHLETS THEOREM
201
THE PRIME NUMBER THEOREM
229
Copyright

RATIONAL APPROXIMATIONS TO REAL NUMBERS
159

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