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The minimum value

Source: Chinese National Olympiad 2009 P4

January 10, 2009
inequalitiessymmetryfunctionalgebrapolynomialabsolute valueinequalities proposed

Problem Statement

Given an integer n>3. n > 3. Let a1,a2,⋯ ,an a_{1},a_{2},\cdots,a_{n} be real numbers satisfying min |a_{i} \minus{} a_{j}| \equal{} 1, 1\le i\le j\le n. Find the minimum value of \sum_{k \equal{} 1}^n|a_{k}|^3.
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