IMO 1959–1966 - Longlisted Problems (individual years unknown) Question 13

(YUG) Let $a_1,a_2,\ldots,a_n$ be positive real numbers. Prove the inequality $$\binom n2\sum_{i<j}\frac1{a_i a_j}\ge4\left(\sum_{i<j}\frac1{a_i+a_j}\right)^2$$ and find the conditions on the numbers $a_i$ for equality to hold.