olymmath

AIME 2001b Problem 8

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A certain function ff has the properties that f(3x)=3f(x)f(3x) = 3f(x) for all positive real values of xx, and that f(x)=1−∣x−2∣f(x) = 1-|x-2| for 1≤x≤31\le x \le 3. Find the smallest xx for which f(x)=f(2001)f(x) = f(2001).

Dataset text AIME 1983 to 2026. Quoted with source.

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