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1971 IMO Problems/Problem 1

Revision as of 13:47, 17 February 2018 by Durianaops (talk | contribs) (Created page with "Prove that the following assertion is true for <math>n=3</math> and <math>n=5</math>, and that it is false for every other natural number <math>n>2:</math> If <math>a_1, a_2,...")
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Prove that the following assertion is true for $n=3$ and $n=5$, and that it is false for every other natural number $n>2:$

If $a_1, a_2,\cdots, a_n$ are arbitrary real numbers, then $(a_1-a_2)(a_1-a_3)\cdots (a_1-a_n)+(a_2-a_1)(a_2-a_3)\cdots (a_2-a_n)+\cdots+(a_n-a_1)(a_n-a_2)\cdots (a_n-a_{n-1})\ge 0.$

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