The USSR Olympiad Problem Book Selected Problems and Theorems of Elementary Mathematics

Over 300 challenging problems in algebra, arithmetic, elementary number theory and trigonometry, selected from the archives of the Mathematical Olympiads held at Moscow University. Most presuppose only high school mathematics but some are of uncommon difficulty and will challenge any mathematician. Complete solutions to all problems. 27 black-and-white illustrations. 1962 edition.

Foreword to the Third (Russian) Edition
Preface to the Second (Russian) Edition
Editor's Foreword to the English Edition
From the Authors
Suggestions for Using this Book
Numerical Reference to the Problems Given in the Moscow Mathematical Olympiads
1. Introductory Problems (1-14)
2. Alterations of Digits in Integers (15-26)
3. The Divisibility of Integers (27-71)
4. Some Problems from Arithmetic (72-109)
5. Equations Having Integer Solutions (110-130)
6. Evaluating Sums and Products (131-159)
7. Miscellaneous Problems from Algebra (160-195)
8. The Algebra of Polynomials (196-221)
9. Complex Numbers (222-239)
10. Some Problems of Number Theory (240-254)
11. Some Distinctive Inequalities (255-308)
12. Difference Sequences and Sums (309-320)
Solutions
Answers and Hints