MathDB
easy inequality

Source: Austria 1988

July 8, 2009
inequalitiesinequalities proposed

Problem Statement

If a1,...,a1988 a_1,...,a_{1988} are positive numbers whose arithmetic mean is 1988 1988, show that: \sqrt[1988]{\displaystyle\prod_{i,j\equal{}1}^{1988} \left( 1\plus{}\frac{a_i}{a_j} \right)} \ge 2^{1988} and determine when equality holds.