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Friendly Introduction to Number Theory, A
ISBN: 9780131861374 | 0131861379
Edition: 3rdFormat: Hardcover
Publisher: Prentice Hall
Pub. Date: 1/1/2006
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Starting with nothing more than basic high school algebra, this volume leads readers gradually from basic algebra to the point of actively performing mathematical research while getting a glimpse of current mathematical frontiers.Features an informal writing style and includes many numerical examples. Emphasizes the methods used for proving theorems rather than specific results. Includes a new chapter on big-Oh notation and how it is used to describe the growth rate of number theoretic functions and to describe the complexity of algorithms. Pro... MORE
| Preface | v | ||||
| Introduction | 1 | (65) | |||
| 6 | (7) | |||
| ... MORE | (7) | |||
| 20 | (4) | |||
| 24 | (4) | |||
| 28 | (7) | |||
| 35 | (9) | |||
| 44 | (9) | |||
| 53 | (7) | |||
| 60 | (6) | |||
| 10 Congruences, Powers, and Euler's Formula | 66 | (4) | |||
| 11 Euler's Phi Function and the Chinese Remainder Theorem | 70 | (8) | |||
| 12 Prime Numbers | 78 | (7) | |||
| 13 Counting Primes | 85 | (6) | |||
| 14 Mersenne Primes | 91 | (4) | |||
| 15 Mersenne Primes and Perfect Numbers | 95 | (10) | |||
| 16 Powers Modulo m and Successive Squaring | 105 | (7) | |||
| 17 Computing kth Roots Modulo m | 112 | (5) | |||
| 18 Powers, Roots, and "Unbreakable" Codes | 117 | (6) | |||
| 19 Primality Testing and Carmichael Numbers | 123 | (11) | |||
| 20 Euler's Phi Function and Sums of Divisors | 134 | (5) | |||
| 21 Powers Modulo p and Primitive Roots | 139 | (10) | |||
| 22 Primitive Roots and Indices | 149 | (7) | |||
| 23 Squares Modulo p | 156 | (8) | |||
| 24 Is -1 a Square Modulo p? Is 2? | 164 | (11) | |||
| 25 Quadratic Reciprocity | 175 | (11) | |||
| 26 Which Primes Are Sums of Two Squares? | 186 | (12) | |||
| 27 Which Numbers Are Sums of Two Squares? | 198 | (6) | |||
| 28 The Equation X4 + Y4 = Z4 | 204 | (3) | |||
| 29 Square-Triangular Numbers Revisited | 207 | (9) | |||
| 30 Pell's Equation | 216 | (6) | |||
| 31 Diophantine Approximation | 222 | (10) | |||
| 32 Diophantine Approximation and Pell's Equation | 232 | (7) | |||
| 33 Number Theory and Imaginary Numbers | 239 | (14) | |||
| 34 The Gaussian Integers and Unique Factorization | 253 | (17) | |||
| 35 Irrational Numbers and Transcendental Numbers | 270 | (16) | |||
| 36 Binomial Coefficients and Pascal's Triangle | 286 | (11) | |||
| 37 Fibonacci's Rabbits and Linear Recurrence Sequences | 297 | (13) | |||
| 38 Oh, What a Beautiful Function | 310 | (14) | |||
| 39 The Topsy-Turvy World of Continued Fractions | 324 | (16) | |||
| 40 Continued Fractions, Square Roots, and Pell's Equation | 340 | (15) | |||
| 41 Generating Functions | 355 | (10) | |||
| 42 Sums of Powers | 365 | (11) | |||
| 43 Cubic Curves and Elliptic Curves | 376 | (12) | |||
| 44 Elliptic Curves with Few Rational Points | 388 | (7) | |||
| 45 Points on Elliptic Curves Modulo p | 395 | (11) | |||
| 46 Torsion Collections Modulo p and Bad Primes | 406 | (4) | |||
| 47 Defect Bounds and Modularity Patterns | 410 | (6) | |||
| 48 Elliptic Curves and Fermat's Last Theorem | 416 | (2) | |||
| Further Reading | 418 | (1) | |||
| A Factorization of Small Composite Integers | 419 | (2) | |||
| B A List of Primes | 421 | (2) | |||
| Index | 423 |
