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Find n s.t the inequality holds for all real numbers x_i

Source: Vietnam NMO 1986 Problem 5

February 6, 2009
inequalitiesfunctioninequalities unsolved

Problem Statement

Find all n>1 n > 1 such that the inequality \sum_{i\equal{}1}^nx_i^2\ge x_n\sum_{i\equal{}1}^{n\minus{}1}x_i holds for all real numbers x1 x_1, x2 x_2, … \ldots, xn x_n.
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