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RU-ALLRUSSIAN 1988 Problem 22

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What is the smallest n for which there is a solution to sin⁡x1+sin⁡x2+…+sin⁡xn=0\sin x_{1} + \sin x_{2} + \ldots +\sin x_{n} = 0 , sin⁡x1+2sin⁡x2+…+nsin⁡xn=100\sin x_{1} + 2 \sin x_{2} + \ldots + n \sin x_{n} = 100 ?

Dataset text NuminaMath olympiads. Quoted with source.

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