Preface Arithmetic of the Integers Induction Division Primes The Chinese Remainder Theorem Thue's Theorem Combinatorial Number Theory Partitions and Generating Functions True Primality Tests Distribution of Primes Modular Arithmetic Basic Properties Modular Perspective Arithmetic Functions: Euler, Carmichael, and Möbius Number and Sums of Divisors The Floor and the Ceiling Polynomial Congruences Primality Testing Cryptology Primitive Roots Order Existence Indices Random Number Generation Public-Key Cryptography Quadratic Residues The Legendre Symbol The Quadratic Reciprocity Law Factoring Simple Continued Fractions and Diophantine Approximation Infinite Simple Continued Fractions Periodic Simple Continued Fractions Pell's Equation and Surds Continued Fractions and Factoring Additivity--Sums of Powers Sums of Two Squares Sums of Three Squares Sums of Four Squares Sums of Cubes Diophantine Equations Norm-Form Equations The Equation ax2+ by2+ cz2= 0 Bachet's Equation Fermat's Last Theorem Appendix A: Fundamental Facts Appendix B: Complexity Appendix C: Primes 9547 and Least Primitive Roots Appendix D: Indices Appendix E: The ABC Conjecture Appendix F: Primes Is in P Solutions to Odd-Numbered Exercises Bibliography List of Symbols Indexprocity Law Factoring Simple Continued Fractions and Diophantine Approximation Infinite Simple Continued Fractions Periodic Simple Continued Fractions Pell's Equation and Surds Continued Fractions and Factoring Additivity--Sums of Powers Sums of Two Squares Sums of Three Squares Sums of Four Squares Sums of Cubes Diophantine Equations Norm-Form Equations The Equation ax2+ by2+ cz2= 0 Bachet's Equation Fermat's Last Theorem Appendix A: Fundamental Facts Appendix B: Complexity Appendix C: Primes 9547 and Least Primitive Roots Appendix D: Indices Appendix E: The ABC Conjecture Appendix F: Primes Is in P Solutions to Odd-Numbered Exercises Bibliography List of Symbols Indexces Appendix E: The ABC Conjecture Appendix F: Primes Is in P Solutions to Odd-Numbered Exercises Bibliography List of Symbols Index.