title: "IMO 1974 LL ROM31" description: "Let y\alpha = n" date: "2026-05-29T11:51:44+07:00" tags: ["imo", "longlist", "mathematics", "olympiad"] categories: ["mathematics"] year: 1974 type: "longlist" origin: "ROM" weight: 197400031 draft: false

IMO 1974 LL ROM31

Origin: ROM

Problem

Let y\alpha = n i=1 x\alpha i , where \alpha ̸= 0, y > 0, xi > 0 are real numbers, and let \lambda ̸= \alpha be a real number. Prove that y\lambda > n i=1 x\lambda i if \alpha(\lambda −\alpha) > 0, and y\lambda < n i=1 x\lambda i if \alpha(\lambda −\alpha) < 0.