Shklyarsky D. Selected Problems and Theorems in Elementary Mathematics...1979
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Shklyarsky D. Selected Problems and Theorems in Elementary Mathematics...1979
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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 (1-29)
Permutation of Digits in a Number (30-45)
Problems in Divisibility of Numbers (46-96)
Miscellaneous Problems in Arithmetic (97-149)
Finding Integral Solutions of Equations (150-171)
Matrices, Sequences and Functions (172-210)
Estimating Sums and Products (211-234)
Miscellaneous Problems in Algebra (235-291)
Algebra of Polynomials (292-320)
Complex Numbers (321-339)
Several Problems in Number Theory (340-350)
Solutions
Answers and Hints