Elementary number theory with applications

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Elementary number theory with applications / Thomas Koshy

資料種別:: 図書
出版情報:: San Diego : Harcourt/Academic Press, c2002
形態:: xix, 716 p. ; 25 cm
著者名:: Koshy, Thomas <DA0636850X>
ISBN:: 9780124211711 [0124211712]
書誌ID:: BA53316822

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注記:

Includes bibliographical references and index

主題:

Number theory

言語:

英語

目次情報:

Preface

A Word to the Student

Fundamentals / 1：

Fundamental Properties / 1.1：

The Summation and Product Notations / 1.2：

Mathematical Induction / 1.3：

Recursion / 1.4：

The Binomial Theorem / 1.5：

Polygonal Numbers / 1.6：

Pyramidal Numbers / 1.7：

Catalan Numbers / 1.8：

Chapter Summary

Review Exercises

Supplementary Exercises

Computer Exercises

Enrichment Readings

Divisibility / 2：

The Division Algorithm / 2.1：

Base-b Representations (optional) / 2.2：

Operations in Nondecimal Bases (optional) / 2.3：

Number Patterns / 2.4：

Prime and Composite Numbers / 2.5：

Fibonacci and Lucas Numbers / 2.6：

Fermat Numbers / 2.7：

Greatest Common Divisors / 3：

Greatest Common Divisor / 3.1：

The Euclidean Algorithm / 3.2：

The Fundamental Theorem of Arithmetic / 3.3：

Least Common Multiple / 3.4：

Linear Diophantine Equations / 3.5：

Congruences / 4：

Linear Congruences / 4.1：

The Pollard Rho Factoring Method / 4.3：

Congruence Applications / 5：

Divisibility Tests / 5.1：

Modular Designs / 5.2：

Check Digits / 5.3：

The p-Queens Puzzle (optional) / 5.4：

Round-Robin Tournaments (optional) / 5.5：

The Perpetual Calendar (optional) / 5.6：

Systems of Linear Congruences / 6：

The Chinese Remainder Theorem / 6.1：

General Linear Systems (optional) / 6.2：

2 x 2 Linear Systems (optional) / 6.3：

Three Classical Milestones / 7：

Wilson's Theorem / 7.1：

Fermat's Little Theorem / 7.2：

Pseudoprimes (optional) / 7.3：

Euler's Theorem / 7.4：

Multiplicative Functions / 8：

Euler's Phi Function Revisited / 8.1：

The Tau and Sigma Functions / 8.2：

Perfect Numbers / 8.3：

Mersenne Primes / 8.4：

The Mobius Function (optional) / 8.5：

Cryptology / 9：

Affine Ciphers / 9.1：

Hill Ciphers / 9.2：

Exponentiation Ciphers / 9.3：

The RSA Cryptosystem / 9.4：

Knapsack Ciphers / 9.5：

Primitive Roots and Indices / 10：

The Order of a Positive Integer / 10.1：

Primality Tests / 10.2：

Primitive Roots for Primes / 10.3：

Composites with Primitive Roots (optional) / 10.4：

The Algebra of Indices / 10.5：

Quadratic Congruences / 11：

Quadratic Residues / 11.1：

The Legendre Symbol / 11.2：

Quadratic Reciprocity / 11.3：

The Jacobi Symbol / 11.4：

Quadratic Congruences with Composite Moduli (optional) / 11.5：

Continued Fractions / 12：

Finite Continued Fractions / 12.1：

Infinite Continued Fractions / 12.2：

Miscellaneous Nonlinear Diophantine Equations / 13：

Pythagorean Triangles / 13.1：

Fermat's Last Theorem / 13.2：

Sums of Squares / 13.3：

Pell's Equation / 13.4：

Appendix

Proof Methods / A.1：

Web Sites / A.2：

Tables

Factor Table / T.1：

Values of Some Arithmetic Functions / T.2：

Least Primitive Roots r Modulo Primes p / T.3：

Indices / T.4：

References

Solutions to Odd-Numbered Exercises

Credits / Chapter 1：

Index

Preface

A Word to the Student

Fundamentals / 1：

Fundamental Properties / 1.1：

The Summation and Product Notations / 1.2：

Mathematical Induction / 1.3：

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