2007;
336 pp;
Hardcover

MSC: Primary 11;

Print ISBN: 978-0-8218-4224-9

Product Code: PINT

List Price: $53.00

Individual Member Price: $42.40

**Electronic ISBN: 978-1-4704-2492-3
Product Code: PINT.E**

List Price: $53.00

Individual Member Price: $42.40

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#### Supplemental Materials

# 1001 Problems in Classical Number Theory

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*Jean-Marie De Koninck; Armel Mercier*

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 or 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.

#### Readership

Undergraduates and graduate students interested in number theory.

#### Reviews & Endorsements

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.

-- Book News, Inc.

#### Table of Contents

# Table of Contents

## 1001 Problems in Classical Number Theory

- Cover Cover11 free
- Title iii4 free
- Copyright iv5 free
- Contents vii8 free
- Distribution of the Problems according to Their Topics ix10 free
- Preface xi12 free
- Part 1. Key Elements from the Theory 114 free
- Notations 316
- Some Classical Forms of Argument 316
- Inequalities 316
- Divisibility 417
- Prime Numbers 518
- Congruences 619
- The Function [x] 720
- Arithmetical Functions 821
- Diophantine Equations 1023
- Quadratic Reciprocity 1023
- Continued Fractions 1124
- Classification of Real Numbers 1225
- Two Conjectures 1225

- Part 2. Statements of the Problems 1326
- Mathematical Induction and Combinatorics 1528
- Divisibility 1932
- Prime Numbers 2538
- Representation of Numbers 3447
- Congruences 3851
- Primality Tests and Factorization Algorithms 4457
- Integer Parts 4962
- Arithmetical Functions 5366
- Solving Equations Involving Arithmetical Functions 7891
- Special Numbers 8194
- Diophantine Equations 8497
- Quadratic Reciprocity 91104
- Continued Fractions 95108
- Classification of Real Numbers 99112

- Part 3. Solutions 103116
- Bibliography 331344
- Subject Index 333346
- Index of Authors 335348 free
- Back Cover Back Cover1350