How Many Values Can It Attain?

Algebra Level 5

Let ff be a function from the positive integers to the positive integers such that f(m+n)+2>f(m)+f(f(n))f(m+n) + 2 > f(m) + f(f(n)) for all positive integers m,n.m,n. Find the last three digits of the sum of all possible values of f(2014).f(2014).

Details and assumptions

  • The inequality is strict.
  • This problem is not original.
  • A typo has been fixed. Sorry for the inconvenience.
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