An Introduction to the Theory of Numbers

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Clarendon Press, 1979 - 426 páginas
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This is the fifth edition of a work (first published in 1938) which has become the standard introduction to the subject. The book has grown out of lectures delivered by the authors at Oxford, Cambridge, Aberdeen, and other universities. It is neither a systematic treatise on the theory ofnumbers nor a 'popular' book for non-mathematical readers. It contains short accounts of the elements of many different sides of the theory, not usually combined in a single volume; and, although it is written for mathematicians, the range of mathematical knowledge presupposed is not greater thanthat of an intelligent first-year student. In this edition the main changes are in the notes at the end of each chapter; Sir Edward Wright seeks to provide up-to-date references for the reader who wishes to pursue a particular topic further and to present, both in the notes and in the text, areasonably accurate account of the present state of knowledge.
 

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Índice

THE SERIES OF PRIMES
1
THE SERIES OF PRIMES
12
FAREY SERIES AND A THEOREM OF MINKOWSKI
23
IRRATIONAL NUMBERS
38
CONGRUENCES AND RESIDUES
48
FERMATS THEOREM AND ITS CONSEQUENCES
63
GENERAL PROPERTIES OF CONGRUENCES
82
THE REPRESENTATION OF NUMBERS BY DECIMALS
107
QUADRATIC FIELDS
218
THE ARITHMETICAL FUNCTIONS fn in dn 7n rn
233
GENERATING FUNCTIONS OF ARITHMETICAL FUNCTIONS
244
THE ORDER OF MAGNITUDE OF ARITHMETICAL FUNCTIONS
260
PARTITIONS
273
THE REPRESENTATION OF A NUMBER BY TWO
297
REPRESENTATION BY CUBES AND HIGHER POWERS
317
THE SERIES OF PRIMES
340

CONTINUED FRACTIONS
129
APPROXIMATION OF IRRATIONALS BY RATIONALS
154
THE FUNDAMENTAL THEOREM OF ARITHMETIC IN kl
178
SOME DIOPHANTINE EQUATIONS
190
QUADRATIC FIELDS
204
KRONECKERS THEOREM
375
APPENDIX
414
INDEX OF SPECIAL SYMBOLS AND WORDS
420
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The Arithmetic of Elliptic Curves
Joseph H. Silverman
No hay vista previa disponible - 1986
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