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What is 1999 National Olympiad Problems about?

This document contains solutions to problems from the 1999 Belarus National Contests. The first problem asks the reader to determine all real numbers a such that the function f(x) = |ax + sinx| is periodic. The solution shows that a must be of the form r/π for some rational number r. The second problem asks the reader to prove inequalities relating the sum of the divisors of an integer n to √n and √2kn, where k is the number of divisors. The third problem involves tiling a 7x7 board with tiles of different

Author

claus160867

Language

EN