IMO 1966 LL YUG13

Let a1, a2, . . . , an be positive real numbers. Prove the inequality

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IMO 1966 LL YUG13

Origin: YUG

Problem

Let a1, a2, . . . , an be positive real numbers. Prove the inequality n   i<j aiaj \geq4 ⎛ ⎝ i<j ai + aj ⎞ ⎠ and find the conditions on the numbers ai for equality to hold.