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Find a,b for which cyclic x_i inequality holds

Source: Baltic Way 1998 Q15

March 19, 2011
inequalitiesinequalities proposed

Problem Statement

For which positive real numbers a,ba,b does the inequality x1x2+x2x3+…xn−1xn+xnx1≥x1ax2bx3a+x2ax3bx4a+…+xnax1bx2ax_1x_2+x_2x_3+\ldots x_{n-1}x_n+x_nx_1\ge x_1^ax_2^bx_3^a+ x_2^ax_3^bx_4^a+\ldots +x_n^ax_1^bx_2^a hold for all integers n>2n>2 and positive real numbers x1,…,xnx_1,\ldots ,x_n?
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