IMO Shortlist 1971 problem 5


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April 2, 2012
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Let E_n=(a_1-a_2)(a_1-a_3)\ldots(a_1-a_n)+(a_2-a_1)(a_2-a_3)\ldots(a_2-a_n)+\ldots+(a_n-a_1)(a_n-a_2)\ldots(a_n-a_{n-1}). Let S_n be the proposition that E_n\ge0 for all real a_i. Prove that S_n is true for n=3 and 5, but for no other n>2.
Source: Međunarodna matematička olimpijada, shortlist 1971