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Inequality in 2n variables with 13th powers

Source: All-Russian MO 2000

December 30, 2012
inequalitiesinequalities unsolvedn-variable inequalityabel formula

Problem Statement

Let −1<x1<x2,⋯<xn<1-1 < x_1 < x_2 , \cdots < x_n < 1 and x113+x213+⋯+xn13=x1+x2+⋯+xnx_1^{13} + x_2^{13} + \cdots + x_n^{13} = x_1 + x_2 + \cdots + x_n. Prove that if y1<y2<⋯<yny_1 < y_2 < \cdots < y_n, then x113y1+⋯+xn13yn<x1y1+x2y2+⋯+xnyn. x_1^{13}y_1 + \cdots + x_n^{13}y_n < x_1y_1 + x_2y_2 + \cdots + x_ny_n.
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