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Fulfill Three Conditions

Source: 2009 MMO Problem #1

September 12, 2011
inequalitiesalgebrasystem of equationsalgebra unsolved

Problem Statement

Determine all integers n≥1n\ge1 for which there exists nn real numbers x1,…,xnx_1,\ldots,x_n in the closed interval [−4,2][-4,2] such that the following three conditions are fulfilled: - the sum of these real numbers is at least nn. - the sum of their squares is at most 4n4n. - the sum of their fourth powers is at least 34n34n. (Proposed by Gerhard Woeginger, Austria)
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