2000 AIME I Problems/Problem 12
Given a function for which holds for all real what is the largest number of different values that can appear in the list
Since we can conclude that (by the Euclidean algorithm)
So we need only to consider one period , which can have at most distinct values which determine the value of at all other integers.
But we also know that , so the values and are repeated. This gives a total of
To show that it is possible to have distinct, we try to find a function which fulfills the given conditions. A bit of trial and error would lead to the cosine function: (in degrees).
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