VMO 1999 Problem 6
Find all functions f(n) defined on the non-negative integers with values in the set {0, 1, 2, ... , 2000} such that: (1) f(n) = n for 0 ≤ n ≤ 2000; and (2) f( f(m) + f(n) ) = f(m + n) for all m, n.
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