MathDB
IMO Long List 1986 with n variables

Source:

August 29, 2010
inequalitiesinequalities proposed

Problem Statement

Given nn real numbers a1a2ana_1 \leq a_2 \leq \cdots \leq a_n, define M_1=\frac 1n \sum_{i=1}^{n} a_i ,   M_2=\frac{2}{n(n-1)} \sum_{1 \leq ia1M1QM1+Qana_1 \leq M_1 - Q \leq M_1 + Q \leq a_n and that equality holds if and only if a1=a2==an.a_1 = a_2 = \cdots = a_n.