Estonian Math Competitions 2005/2006
Source: Juniors Problem 9
July 30, 2008
inequalitiesinequalities unsolved
Problem Statement
Let a, b, c be positive integers. Prove that the inequality
(x\minus{}y)^a(x\minus{}z)^b(y\minus{}z)^c \ge 0
holds for all reals x, y, z if and only if a, b, c are even.