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.
Jean-Marie De Koninck, Université Laval, Quebec, QC, Canada Armel Mercier, Université du Québec à Chicoutimi, QC, Canada
Distribution of the Problems according to Their Topics Preface Part 1. Key Elements from the Theory Notations Some Classical Forms of Argument Inequalities Divisibility Prime Numbers Congruences The Function [x] Arithmetical Functions Diophantine Equations Quadratic Reciprocity Continued Fractions Classification of Real Numbers Two Conjectures Part 2. Statements of the Problems Mathematical Induction and Combinatorics Divisibility Prime Numbers Representation of Numbers Congruences Primality Tests and Factorization Algorithms Integer Parts Arithmetical Functions Solving Equations Involving Arithmetical Functions Special Numbers Diophantine Equations Quadratic Reciprocity Continued Fractions Classification of Real Numbers Part 3. Solutions Bibliography Subject Index Index of Authors