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For which n does the inequality hold?

Source: Baltic Way 1999

December 23, 2010
inequalitiesinequalities proposed

Problem Statement

Determine all positive integers n≥3n\ge 3 such that the inequality a1a2+a2a3+…an−1an≤0a_1a_2+a_2a_3+\ldots a_{n-1}a_n\le 0 holds for all real numbers a1,a2,…,ana_1,a_2,\ldots , a_n which satisfy a1+a2+…+an=0a_1+a_2+\ldots +a_n=0.
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