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If and only if

Source: Chinese TST

April 6, 2008
inequalities proposedinequalities

Problem Statement

For a given integer n≥2, n\geq 2, determine the necessary and sufficient conditions that real numbers a1,a2,⋯ ,an, a_{1},a_{2},\cdots, a_{n}, not all zero satisfy such that there exist integers 0<x1<x2<⋯<xn, 0<x_{1}<x_{2}<\cdots<x_{n}, satisfying a_{1}x_{1}\plus{}a_{2}x_{2}\plus{}\cdots\plus{}a_{n}x_{n}\geq 0.
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