Fundamental Number Theory with Applications,

An update of the most accessible introductory number theory text available, Fundamental Number Theory with Applications, Second Editionpresents a mathematically rigorous yet easy-to-follow treatment of the fundamentals and applications of the subject. This edition removes all advanced material to be even more accessible in scope; adds new fundamental material, including partition theory, generating functions, and combinatorial number theory; and expands coverage of random number generation, Diophantine analysis, and additive number theory. It also includes more applications to cryptography, primality testing, and factoring as well as nearly 70 biographies of major contributors to the field.

Richard A. Mollin, Ph.D., is a professor in the mathematics department at the University of Calgary, Alberta, Canada

Preface	p. ix
Arithmetic of the Integers	p. 1
Induction	p. 1
Division	p. 16
Primes	p. 30
The Chinese Remainder Theorem	p. 40
Thue's Theorem	p. 44
Combinatorial Number Theory	p. 49
Partitions and Generating Functions	p. 55
True Primality Tests	p. 60
Distribution of Primes	p. 65
Modular Arithmetic	p. 73
Basic Properties	p. 73
Modular Perspective	p. 84
Arithmetic Functions: Euler, Carmichael, and Mobius	p. 90
Number and Sums of Divisors	p. 102
The Floor and the Ceiling	p. 108
Polynomial Congruences	p. 113
Primality Testing	p. 119
Cryptology	p. 127
Primitive Roots	p. 139
Order	p. 139
Existence	p. 145
Indices	p. 153
Random Number Generation	p. 160
Public-Key Cryptography	p. 166
Quadratic Residues	p. 177
The Legendre Symbol	p. 177
The Quadratic Reciprocity Law	p. 189
Factoring	p. 201
Simple Continued Fractions and Diophantine Approximation	p. 209
Infinite Simple Continued Fractions	p. 209
Periodic Simple Continued Fractions	p. 221
Pell's Equation and Surds	p. 232
Continued Fractions and Factoring	p. 240
Additivity - Sums of Powers	p. 243
Sums of Two Squares	p. 243
Sums of Three Squares	p. 252
Sums of Four Squares	p. 254
Sums of Cubes	p. 259
Diophantine Equations	p. 265
Norm-Form Equations	p. 265
The Equation ax[superscript 2] + by[superscript 2] + cz[superscript 2] = 0	p. 274
Bachet's Equation	p. 277
Fermat's Last Theorem	p. 281
Fundamental Facts	p. 285
Complexity	p. 311
Primes [characters not reproducible] 9547 and Least Primitive Roots	p. 313
Indices	p. 318
The ABC Conjecture	p. 319
Primes is in P	p. 320
Solutions to Odd-Numbered Exercises	p. 323
Bibliography	p. 351
List of Symbols	p. 355
Index	p. 356
About the Author	p. 369
Table of Contents provided by Ingram. All Rights Reserved.

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Fundamental Number Theory with Applications, Second Edition

Summary

Author Biography

Table of Contents

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