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Find maximum of the sum

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September 15, 2010
algebramaximizationoptimizationlagrangecalculusIMO ShortlistIMO Longlist

Problem Statement

Given the integer n>1n > 1 and the real number a>0a > 0 determine the maximum of ∑i=1n−1xixi+1\sum_{i=1}^{n-1} x_i x_{i+1} taken over all nonnegative numbers xix_i with sum a.a.
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