MathDB

19

Part of 1982 IMO Shortlist

Problems(1)

Prove that z exists

Source: IMO LongList 1982 - P22

9/10/2010
Let MM be the set of real numbers of the form m+nm2+n2\frac{m+n}{\sqrt{m^2+n^2}}, where mm and nn are positive integers. Prove that for every pair x∈M,y∈Mx \in M, y \in M with x<yx < y, there exists an element z∈Mz \in M such that x<z<y.x < z < y.
functiontopologyalgebraDiscrete intermediate value theoremIMO ShortlistIMO Longlist