Front cover -- Elementary Number Theory with Applications -- Copyright page -- Contents -- Preface -- A Word to the Student -- Chapter 1. Fundamentals -- 1.1 Fundamental Properties -- 1.2 The Summation and Product Notations -- 1.3 Mathematical Induction -- 1.4 Recursion -- 1.5 The Binomial Theorem -- 1.6 Polygonal Numbers -- 1.7 Pyramidal Numbers -- 1.8 Catalan Numbers -- Chapter Summary -- Review Exercises -- Supplementary Exercises -- Computer Exercises -- Enrichment Readings -- Chapter 2. Divisibility -- 2.1 The Division Algorithm -- *2.2 Base-b Representations (optional) -- *2.3 Operations in Nondecimal Bases (optional) -- 2.4 Number Patterns -- 2.5 Prime and Composite Numbers -- 2.6 Fibonacci and Lucas Numbers -- 2.7 Fermat Numbers -- Chapter Summary -- Review Exercises -- Supplementary Exercises -- Computer Exercises -- Enrichment Readings -- Chapter 3. Greatest Common Divisors -- 3.1 Greatest Common Divisor -- 3.2 The Euclidean Algorithm -- 3.3 The Fundamental Theorem of Arithmetic -- 3.4 Least Common Multiple -- 3.5 Linear Diophantine Equations -- Chapter Summary -- Review Exercises -- Supplementary Exercises -- Computer Exercises -- Enrichment Readings -- Chapter 4. Congruences -- 4.1 Congruences -- 4.2 Linear Congruences -- 4.3 The Pollard Rho Factoring Method -- Chapter Summary -- Review Exercises -- Supplementary Exercises -- Computer Exercises -- Enrichment Readings -- Chapter 5. Congruence Applications -- 5.1 Divisibility Tests -- 5.2 Modular Designs -- 5.3 Check Digits -- *5.4 The p-Queens Puzzle (optional) -- *5.5 Round-Robin Tournaments (optional) -- *5.6 The Perpetual Calendar (optional) -- Chapter Summary -- Review Exercises -- Supplementary Exercises -- Computer Exercises -- Enrichment Readings -- Chapter 6. Systems of Linear Congruences -- 6.1 The Chinese Remainder Theorem -- *6.2 General Linear Systems (optional).

*6.3 2x2 Linear Systems (optional) -- Chapter Summary -- Review Exercises -- Supplementary Exercises -- Computer Exercises -- Enrichment Readings -- Chapter 7. Three Classical Milestones -- 7.1 Wilson's Theorem -- 7.2 Fermat's Little Theorem -- *7.3 Pseudoprimes (optional) -- 7.4 Euler's Theorem -- Chapter Summary -- Review Exercises -- Supplementary Exercises -- Computer Exercises -- Enrichment Readings -- Chapter 8. Multiplicative Functions -- 8.1 Euler's Phi Function Revisited -- 8.2 The Tau and Sigma Functions -- 8.3 Perfect Numbers -- 8.4 Mersenne Primes -- *8.5 The Möbius Function (optional) -- Chapter Summary -- Review Exercises -- Supplementary Exercises -- Computer Exercises -- Enrichment Readings -- Chapter 9. Cryptology -- 9.1 Affine Ciphers -- 9.2 Hill Ciphers -- 9.3 Exponentiation Ciphers -- 9.4 The RSA Cryptosystem -- 9.5 Knapsack Ciphers -- Chapter Summary -- Review Exercises -- Supplementary Exercises -- Computer Exercises -- Enrichment Readings -- Chapter 10. Primitive Roots and Indices -- 10.1 The Order of a Positive Integer -- 10.2 Primality Tests -- 10.3 Primitive Roots for Primes -- *10.4 Composites with Primitive Roots (optional) -- 10.5 The Algebra of Indices -- Chapter Summary -- Review Exercises -- Supplementary Exercises -- Computer Exercises -- Enrichment Readings -- Chapter 11. Quadratic Congruences -- 11.1 Quadratic Residues -- 11.2 The Legendre Symbol -- 11.3 Quadratic Reciprocity -- 11.4 The Jacobi Symbol -- *11.5 Quadratic Congruences with Composite Moduli (optional) -- Chapter Summary -- Review Exercises -- Supplementary Exercises -- Computer Exercises -- Enrichment Readings -- Chapter 12. Continued Fractions -- 12.1 Finite Continued Fractions -- 12.2 Infinite Continued Fractions -- Chapter Summary -- Review Exercises -- Supplementary Exercises -- Computer Exercises -- Enrichment Readings.

Chapter 13. Miscellaneous Nonlinear Diophantine Equations -- 13.1 Pythagorean Triangles -- 13.2 Fermat's Last Theorem -- 13.3 Sums of Squares -- 13.4 Pell's Equation -- Chapter Summary -- Review Exercises -- Supplementary Exercises -- Computer Exercises -- Enrichment Readings -- Appendix -- A.1 Proof Methods -- A.2 Web Sites -- Tables -- T.1 Factor Table -- T.2 Values of Some Arithmetic Functions -- T.3 Least Primitive Roots r Modulo Primes p -- T.4 Indices -- References -- Solutions to Odd-Numbered Exercises -- Chapter 1 Fundamentals -- Chapter 2 Divisibility -- Chapter 3 Greatest Common Divisors -- Chapter 4 Congruences -- Chapter 5 Congruence Applications -- Chapter 6 Systems of Linear Congruences -- Chapter 7 Three Classical Milestones -- Chapter 8 Multiplicative Functions -- Chapter 9 Cryptology -- Chapter 10 Primitive Roots and Indices -- Chapter 11 Quadratic Congruences -- Chapter 12 Continued Fractions -- Chapter 13 Miscellaneous Nonlinear Diophantine Equations -- Credits -- Index.