ÖMO 1988 Problem 1

If $a_1,...,a_{1988}$ are positive numbers whose arithmetic mean is $1988$ , show that:

$\sqrt[1988]{ \prod_{i,j=1}^{1988} \left( 1+\frac{a_i}{a_j} \right)} \ge 2^{1988}$

and determine when equality holds.