1001 Problems in Classical Number Theory

There really are 1001 problems in classical number theory here, and each one leads to the next so readers can progress at their own speed. As they read they will be enticed into trying just one more, succeeding, and moving on to the next, Ideal for self-study or for a year's worth of exercises, this starts with key elements from the theory such as argument, inequalities, divisibility, prime numbers, congruence, arithmetic functions, diophantine equations, and classifications of real numbers. The authors then work through the problems together with readers following basically the sequence in the text and providing solutions. The result is quite accessible and the innovative approach could serve as a model for a lively series. Annotation 2007 Book News, Inc., Portland, OR (booknews.com) Title Contents Distribution of the Problems according to Their Topics Preface Part 1: Key Elements from the Theory Part 2: Statements of the Problems 1. Mathematical Induction and Combinatorics 2. Divisibility 3. Prime Numbers 4. Representations of Numbers 5. Congruences 6. Primality Tests and Factorization Algorithms 7. Integer Parts 8. Arithmetical Functions 9. Solving Equations Involving Arithmetical Functions 10. Special Numbers 11. Diophantine Equations 12. Quadratic Reciprocity 13. Continued Fractions 14. Classification of Real Numbers Part 3: Solutions 1. Mathematical Induction and Combinatorics 2. Divisibility 3. Prime Numbers 4. Representations of Numbers 5. Congruences 6. Primality Tests and Factorization Algorithms 7. Integer Parts 8. Arithmetical Functions 9. Solving Equations Involving Arithmetical Functions 10. Special Numbers 11. Diophantine Equations 12. Quadratic Reciprocity 13. Continued Fractions 14. Classification of Real Numbers Bibliography Subject Index Index of Authors "In the spirit of The Book of the One Thousand and One Nights, the authors offer 1001 problems in number theory in a way that entices the reader to immediately attack the next problem. Whether a novice of an experienced mathematician, anyone fascinated by numbers will find a great variety of problems - some simple, others more complex - that will provide them with a wonderful mathematical experience."--Jacket