# How Many Values Can It Attain?

Algebra Level 5

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

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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