Elementary Theory of Numbers: Second English Edition (edited by A. Schinzel)

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Elsevier, Feb 1, 1988 - Mathematics - 513 pages
Since the publication of the first edition of this work, considerable progress has been made in many of the questions examined. This edition has been updated and enlarged, and the bibliography has been revised.

The variety of topics covered here includes divisibility, diophantine equations, prime numbers (especially Mersenne and Fermat primes), the basic arithmetic functions, congruences, the quadratic reciprocity law, expansion of real numbers into decimal fractions, decomposition of integers into sums of powers, some other problems of the additive theory of numbers and the theory of Gaussian integers.

 

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Contents

Chapter I Divisibility and Indeterminate Equations of First Degree
1
Chapter II Diophantlne Analysis of Second and Higher Degrees
32
Chapter III Prime Numbers
113
Chapter IV Number of Divisors and Their Sum
166
Chapter V Congruences
198
Chapter VI EulerS Totient Function and The Theorem of Euler
245
Chapter VII Representation of Numbers Bydecimals in a Given Scale
285
Chapter VIII Continued Fractions
304
Chapter X Mersenne Numbers and Fermat Numbers
360
Chapter XI Representations of Natural Numbers as Sums of Non negative kth Powers
378
Chapter XII Some Problems of the Additive Theory of Numbers
431
Chapter XIII Complex Integers
449
Bibliography
482
Author index
505
Subject index
511
Addendum and Corrigendum Inserted in July 1987
514

Chapter IX LegendreS Symbol and Jacobis Symbol
340

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