In this post we will see Selected Problems and Theorems in
Elementary Mathematics – Arithmetic and Algebra by D. O. Shklyarsky,  N. N. Chentsov and I. M. Yaglom. This is another book in the  Problems and Solutions series.

This book contains the conditions of problems, the answers and hints  to them and the solutions of the problems. The conditions of the most difficult problems are marked by stars.

We recommend the reader to start with trying to solve without
assistance the problem he is interested in. In case this attempt
fails he can read the hint or the answer to the problem, which may
facilitate the solution, Finally, if this does not help, the
solution of the problem given in the book should be studied. However, for the starred problems it may turn out to be appropriate to begin with reading the hints or the answers before proceeding to solve the problems.

Most of the problems in the book are independent of one another
except those in the last two sections (“Complex Numbers” and
“Several Problems in Number Theory”) where the problems are more  closely interrelated.

It is advisable to choose a definite section ot the book and to spend some time on solving the problems of that section. Only alter that (this does not of course mean that all the problems or most of the problems must necessarily be solved) should the reader pass to another section and so on. However, the order in which the sections are arranged in the book may not be followed. The solutions of some
problems include indications concerning possible generalisations of the conditions of the problems. The reader is advised to think of similar generalizations for other problems; it is also interesting to try to state new problems akin to those collected in this book.

This book was translated from the Russian by V. M. Volosov and
I. G. Volosova. The book was published by first Mir Publishers in
1978.

All credits to the original uploader.

PDF | 15.3 MB | Pages: 432 | Bookmarked | OCR
You can get the book here

Table of Contents
Preface 5
Instructions 8
Problems 9
1. Introductory Problems (I-29) 9
2. Permutation of Digits in a Number (30-45) 16
3. Problems in Divisibility of Numbers (46-96) 17
4. Miscellaneous Problems in Arithmetic (97-149) 23
5. Finding Integral Solutions of Equations (150.171) 31
6. Matrices, Sequences and Functions (172-210) 84
7. Estimating Sums snd Products (211-234) 44
8. Miscellaneous Problems ln Algebra (235-291 ) 50
9. Algebra of Polynomia!s (292-320) 59
10. Complex Numbers (321-339) 63
11. Several Problems in Number Theory (340.350) 67
Solutions 71
Answers and Hints 412