## The USSR Olympiad Problem Book – Shklarsky, Chentzov, Yaglom

In this post, we will see the book The USSR Olympiad Problem Book by D. O. Shklarsky, N. N. Chentzov and I. M. Yaglom.

This book contains 320 unconventional problems in algebra, arithme­tic, elementary number theory, and trigonometry. Most of these problems first appeared in competitive examinations sponsored by the School Mathematical Society of the Moscow State University and in the Mathematical Olympiads held in Moscow. The book is designed for students having a mathematical background at the high school level ;T very many of the problems are within reach of seventh and eighth grade students of outstanding ability. Solutions are given for all the problems. The solutions for the more difficult problems are especially detailed.

The book was translated from Russian by John Maykovich and edited by Irving Sussman and was published in 1962.

You can get the book here.

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# Contents

Foreword to the Third (Russian) Edition v
Preface to the Second (Russian) Edition vii
Editor’s Foreword to the English Edition xi

From the Authors 1
Suggestions for Using this Book 3
Numerical Reference to the Problems Given in the Moscow Mathematical Olympiads 5

1. Introductory Problems (1-14) 6
2. Alterations of Digits in Integers (15-26) 11
3. The Divisibility of Integers (27-71) 13
4. Some Problems from Arithmetic (72-109) 20
5. Equations Having Integer Solutions (110-130) 27
6. Evaluating Sums and Products (131-159) 30
7. Miscellaneous Problems from Algebra (160-195) 38
8. The Algebra of Polynomials (196-221) 45
9. Complex Numbers (222-239) 50
10. Some Problems of Number Theory (240-254) 56
11. Some Distinctive Inequalities (255-308) 61
12. Difference Sequences and Sums (309-320) 74

Solutions 80