olymmath

AIME 2000a Problem 12

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Given a function ff for which f(x)=f(398−x)=f(2158−x)=f(3214−x)f(x) = f(398 - x) = f(2158 - x) = f(3214 - x) holds for all real x,x, what is the largest number of different values that can appear in the list f(0),f(1),f(2),…,f(999)?f(0),f(1),f(2),\ldots,f(999)?

Dataset text AIME 1983 to 2026. Quoted with source.

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