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Nice nondecreasing function

Source: RMO 2008, 11th Grade, Problem 1

April 30, 2008
functionreal analysisreal analysis unsolved

Problem Statement

Let f:(0,∞)→R f : (0,\infty) \to \mathbb R be a continous function such that the sequences {f(nx)}n≥1 \{f(nx)\}_{n\geq 1} are nondecreasing for any real number x x. Prove that f f is nondecreasing.
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