title: "IMO 1992 LL ROM62" description: 'Let c1, . . . , cn (n \geq2) be real numbers such that 0 \leq ci \leqn.' date: "2026-05-29T11:51:44+07:00" tags: ["imo", "longlist", "mathematics", "olympiad"] categories: ["mathematics"] year: 1992 type: "longlist" origin: "ROM" weight: 199200062 draft: false

IMO 1992 LL ROM62

Origin: ROM

Problem

Let c1, . . . , cn (n \geq2) be real numbers such that 0 \leq ci \leqn. Prove that there exist integers x1, . . . , xn such that  ki = 0 and 1−n \leq ci + nki \leqn for every i = 1, . . . , n.