What Is Number Theory? |
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1 | (4) |
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5 | (38) |
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6 | (10) |
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16 | (7) |
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23 | (7) |
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30 | (7) |
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37 | (6) |
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Integer Representations and Operations |
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43 | (24) |
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Representations of Integers |
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43 | (10) |
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Computer Operations with Integers |
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53 | (7) |
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Complexity of Integer Operations |
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60 | (7) |
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Primes and Greatest Common Divisors |
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67 | (74) |
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68 | (9) |
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The Distribution of Primes |
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77 | (13) |
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90 | (7) |
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97 | (11) |
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The Fundamental Theorem of Arithmetic |
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108 | (15) |
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Factorization Methods and the Fermat Numbers |
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123 | (10) |
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Linear Diophantine Equations |
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133 | (8) |
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141 | (48) |
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Introduction to Congruences |
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141 | (12) |
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153 | (5) |
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The Chinese Remainder Theorem |
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158 | (10) |
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Solving Polynomial Congruences |
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168 | (6) |
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Systems of Linear Congruences |
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174 | (10) |
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Factoring Using the Pollard Rho Method |
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184 | (5) |
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Applications of Congruences |
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189 | (26) |
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189 | (6) |
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195 | (5) |
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200 | (2) |
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202 | (5) |
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207 | (8) |
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215 | (24) |
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Wilson's Theorem and Fermat's Little Theorem |
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215 | (8) |
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223 | (10) |
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233 | (6) |
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239 | (38) |
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239 | (11) |
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The Sum and Number of Divisors |
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250 | (7) |
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Perfect Numbers and Mersenne Primes |
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257 | (12) |
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269 | (8) |
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277 | (56) |
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278 | (8) |
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286 | (19) |
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305 | (3) |
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308 | (8) |
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316 | (7) |
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Cryptographic Protocols and Applications |
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323 | (10) |
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333 | (46) |
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The Order of an Integer and Primitive Roots |
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334 | (7) |
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Primitive Roots for Primes |
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341 | (6) |
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The Existence of Primitive Roots |
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347 | (8) |
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355 | (10) |
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Primality Tests Using Orders of Integers and Primitive Roots |
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365 | (7) |
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372 | (7) |
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Applications of Primitive Roots and the Order of an Integer |
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379 | (22) |
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379 | (10) |
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389 | (5) |
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An Application to the Splicing of Telephone Cables |
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394 | (7) |
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401 | (54) |
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Quadratic Residues and Nonresidues |
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402 | (15) |
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The Law of Quadratic Reciprocity |
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417 | (13) |
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430 | (9) |
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439 | (9) |
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448 | (7) |
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Decimal Fractions and Continued Fractions |
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455 | (54) |
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455 | (13) |
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Finite Continued Fractions |
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468 | (10) |
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Infinite Continued Fractions |
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478 | (12) |
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Periodic Continued Fractions |
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490 | (14) |
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Factoring Using Continued Fractions |
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504 | (5) |
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Some Nonlinear Diophantine Equations |
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509 | (38) |
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510 | (6) |
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516 | (12) |
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528 | (11) |
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539 | (8) |
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547 | (30) |
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Gaussian Integers and Gaussian Primes |
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547 | (12) |
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Greatest Common Divisors and Unique Factorization |
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559 | (11) |
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Gaussian Integers and Sums of Squares |
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570 | (7) |
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A Axioms for the Set of Integers |
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577 | (4) |
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581 | (8) |
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C Using Maple and Mathematica for Number Theory |
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589 | (10) |
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Using Maple for Number Theory |
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589 | (4) |
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Using Mathematica for Number Theory |
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593 | (6) |
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D Number Theory Web Links |
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599 | (2) |
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601 | (16) |
Answers to Odd-Numbered Exercises |
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617 | (72) |
Bibliography |
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689 | (14) |
Index of Biographies |
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703 | (2) |
Index |
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705 | (16) |
Photo Credits |
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721 | |