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Table of Contents
|Flowchart of Chapter Dependencies||p. ix|
|What Is Number Theory?||p. 6|
|Pythagorean Triples||p. 13|
|Pythagorean Triples and the Unit Circle||p. 21|
|Sums of Higher Powers and Fermat's Last Theorem||p. 26|
|Divisibility and the Greatest Common Divisor||p. 30|
|Linear Equations and the Greatest Common Divisor||p. 37|
|Factorization and the Fundamental Theorem of Arithmetic||p. 46|
|Congruences, Powers, and Fermat's Little Theorem||p. 65|
|Congruences, Powers, and Euler's Formula||p. 71|
|Euler's Phi Function and the Chinese Remainder Theorem||p. 75|
|Prime Numbers||p. 83|
|Counting Primes||p. 90|
|Mersenne Primes||p. 96|
|Mersenne Primes and Perfect Numbers||p. 101|
|Powers Modulo m and Successive Squaring||p. 111|
|Computing kth Roots Modulo m||p. 118|
|Powers, Roots, and "Unbreakable" Codes||p. 123|
|Primality Testing and Carmichael Numbers||p. 129|
|Squares Modulo p||p. 141|
|Is-1 a Square Modulo p? Is 2?||p. 148|
|Quadratic Reciprocity||p. 159|
|Proof of Quadratic Reciprocity||p. 171|
|Which Primes Are Sums of Two Squares?||p. 181|
|Which Numbers Are Sums of Two Squares?||p. 193|
|As Easy as One, Two, Three||p. 199|
|Euler's Phi Function and Sums of Divisors||p. 206|
|Powers Modulo p and Primitive Roots||p. 211|
|Primitive Roots and Indices||p. 224|
|The Equation X4+Y4=Z4||p. 231|
|Square-Triangular Numbers Revisited||p. 236|
|Pell's Equation||p. 245|
|Diophantine Approximation||p. 251|
|Diophantine Approximation and Pell's Equation||p. 260|
|Number Theory and Imaginary Numbers||p. 267|
|The Gaussian Integers and Unique Factorization||p. 281|
|Irrational Numbers and Transcendental Numbers||p. 297|
|Binomial Coefficients and Pascal's Triangle||p. 313|
|Fibonacci's Rabbits and Linear Recurrence Sequences||p. 324|
|Oh, What a Beautiful Function||p. 339|
|Cubic Curves and Elliptic Curves||p. 353|
|Elliptic Curves with Few Rational Points||p. 366|
|Points on Elliptic Curves Modulo p||p. 373|
|Torsion Collections Modulo p and Bad Primes||p. 384|
|Defect Bounds and Modularity Patterns||p. 388|
|Elliptic Curves and Fermat's Last Theorem||p. 394|
|Further Reading||p. 396|
|The Topsy-Turvy World of Continued Fractions [online]||p. 410|
|Continued Fractions and Pell's Equation [online]||p. 426|
|Generating Functions [online]||p. 442|
|Sums of Powers [online]||p. 452|
|Factorization of Small Composite Integers [online]||p. 464|
|A List of Primes [online]||p. 466|
|Table of Contents provided by Ingram. All Rights Reserved.|