Shklyarsky D.O., Chentsov N.N., Yaglom I.M. Selected problems and theorems in elementary mathematics. Aritlimetic and Alqebra

Translated from Russian by V.M. Volosov, I.G. Volosova. — Moscow: Mir Publishers, 1979. — 432 р.The present book contains 350 problems selected from the material of the mathematical olympiads and school mathematics hobby groups in Moscow. About 15 problems have been taken from the manuscript of the late D.O. Shklyarsky (1918-1942), one of the founders of the mathematics hobby group for pupils at the State University of Moscow. It is a great pleasure to thank I. Bernstein, N. Vasilyev, G. Galperin, Yu. Ionin, A. Leman, A. Savin, A. Tolpygo, A. Toom, V. Gutenmacher, L. Makar-Limanov and L.I. Golovina for valuable advice and he! p in the preparation of the book.Preface
Instructions
Problems
Introductory Problems
Permutation of Digits in a Number
Problems in Divisibility of Numbers
Miscellaneous Problems in Arithmetic
Finding Integral Solutions of Equations
Matrices, Sequences and Functions
Estimating Sums and Products
Miscellaneous Problems in Algebra
Algebra of Polynomials
Complex Numbers
Several Problems in Number Theory
Solutions
Answers and Hints