Elementary number theory

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Elementary number theory / David M. Burton

版:: 7th ed., international ed.
資料種別:: 図書
出版情報:: New York : McGraw-Hill, c2011
形態:: xii, 436 p. ; 24 cm
著者名:: Burton, David M. <DA03168752>
ISBN:: 9780071289191 [0071289194]
書誌ID:: BB17238835

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注記:

Includes bibliographical references (p. 387-392) and index

主題:

Number theory

言語:

英語

目次情報:

Preface

New to this Edition

Preliminaries / 1：

Mathematical Induction / 1.1：

The Binomial Theorem / 1.2：

Divisibility Theory in the Integers / 2：

Early Number Theory / 2.1：

The Division Algorithm / 2.2：

The Greatest Common Divisor / 2.3：

The Euclidean Algorithm / 2.4：

The Diophantine Equation / 2.5：

Primes and Their Distribution / 3：

The Fundamental Theorem of Arithmetic / 3.1：

The Sieve of Eratosthenes / 3.2：

The Goldbach Conjecture / 3.3：

The Theory of Congruences / 4：

Carl Friedrich Gauss / 4.1：

Basic Properties of Congruence / 4.2：

Binary and Decimal Representations of Integers / 4.3：

Linear Congruences and the Chinese Remainder Theorem / 4.4：

Fermat's Theorem / 5：

Pierre de Fermat / 5.1：

Fermat's Little Theorem and Pseudoprimes / 5.2：

Wilson's Theorem / 5.3：

The Fermat-Kraitchik Factorization Method / 5.4：

Number-Theoretic Functions / 6：

The Sum and Number of Divisors / 6.1：

The Mbius Inversion Formula / 6.2：

The Greatest Integer Function / 6.3：

An Application to the Calendar / 6.4：

Euler's Generalization of Fermat's Theorem / 7：

Leonhard Euler / 7.1：

Euler's Phi-Function / 7.2：

Euler's Theorem / 7.3：

Some Properties of the Phi-Function / 7.4：

Primitive Roots and Indices / 8：

The Order of an Integer Modulo n / 8.1：

Primitive Roots for Primes / 8.2：

Composite Numbers Having Primitive Roots / 8.3：

The Theory of Indices / 8.4：

The Quadratic Reciprocity Law / 9：

Euler's Criterion / 9.1：

The Legendre Symbol and Its Properties / 9.2：

Quadratic Reciprocity / 9.3：

Quadratic Congruences with Composite Moduli / 9.4：

Introduction to Cryptography / 10：

From Caesar Cipher to Public Key Cryptography / 10.1：

The Knapsack Cryptosystem / 10.2：

An Application of Primitive Roots to Cryptography / 10.3：

Numbers of Special Form / 11：

Marin Mersenne / 11.1：

Perfect Numbers / 11.2：

Mersenne Primes and Amicable Numbers / 11.3：

Fermat Numbers / 11.4：

Certain Nonlinear Diophantine Equations / 12：

The Equation / 12.1：

Fermat's Last Theorem / 12.2：

Representation of Integers as Sums of Squares / 13：

Joseph Louis Lagrange / 13.1：

Sums of Two Squares / 13.2：

Sums of More Than Two Squares / 13.3：

Fibonacci Numbers / 14：

Fibonacci / 14.1：

The Fibonacci Sequence / 14.2：

Certain Identities Involving Fibonacci Numbers / 14.3：

Continued Fractions / 15：

Srinivasa Ramanujan / 15.1：

Finite Continued Fractions / 15.2：

Infinite Continued Fractions / 15.3：

Farey Fractions / 15.4：

Pell's Equation / 15.5：

Some Recent Developments / 16：

Hardy, Dickson, and Erds / 16.1：

Primality Testing and Factorization / 16.2：

An Application to Factoring: Remote Coin Flipping / 16.3：

The Prime Number Theorem and Zeta Function Miscellaneous Problems / 16.4：

Appendixes

General References

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