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38th Austrian Mathematical Competition 2007

Source: round2 problem2 - find highest value C(n)

February 7, 2009

inequalities unsolvedinequalities

Problem Statement

For every positive integer

n

determine the highest value

C(n)

, such that for every

n

-tuple

(a_1,a_2,\ldots,a_n)

of pairwise distinct integers (n \plus{} 1)\sum_{j \equal{} 1}^n a_j^2 \minus{} \left(\sum_{j \equal{} 1}^n a_j\right)^2\geq C(n)