4th All Russian Mathematical Olympiad Problems 1964

4th All Russian Mathematical Olympiad Problems 19641.  In the triangle ABC, the length of the altitude from A is not less than BC, and the length of the altitude from B is not less than AC. Find the angles. 2.  If m, k, n are natural numbers and n>1, prove that we cannot have m(m+1) = kn. 3.  Reduce each of the first billion natural numbers (billion = 109)