2000 AIME II Problems/Problem 12

Problem

Given a function $f$ for which

$f(x) = f(398 - x) = f(2158 - x) = f(3214 - x)$

holds for all real $x,$ what is the largest number of different values that can appear in the list $f(0),f(1),f(2),\ldots,f(999)$ ?

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2000 AIME II (Problems • Answer Key • Resources)
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