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Problems > High School Math > 2003

An Increasing Function for the New Year

Let f be a function from Z+ to Z+ where Z+ is the set of positive integers, such that f satisfies these two conditions:

 

(1) f(n+1) > f(n); that is, f is strictly increasing

 

And

 

(2) f(n+f(m)) = f(n)+m+1

 

 

Find all values of f(2003)

 



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