10

Part of 2006 Estonia Math Open Junior Contests

Problems(1)

Estonian Math Competitions 2005/2006

Source: Juniors Problem 9

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.

inequalitiesinequalities unsolved