easy inequality
Source: Austria 1988
July 8, 2009
inequalitiesinequalities proposed
Problem Statement
If are positive numbers whose arithmetic mean is , 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.