Problem

Source: Chinese TST

Tags: inequalities proposed, inequalities



For a given integer $ n\geq 2,$ determine the necessary and sufficient conditions that real numbers $ a_{1},a_{2},\cdots, a_{n},$ not all zero satisfy such that there exist integers $ 0<x_{1}<x_{2}<\cdots<x_{n},$ satisfying $ a_{1}x_{1}+a_{2}x_{2}+\cdots+a_{n}x_{n}\geq 0.$