IMO Shortlist 1988 problem 19
Dodao/la:
arhiva2. travnja 2012. Let
![f(n)](/media/m/d/3/e/d3e47283bffbbf24c97f0c6474d5a82d.png)
be a function defined on the set of all positive integers and having its values in the same set. Suppose that
![f(f(n) + f(m)) = m + n](/media/m/5/0/4/504f620ca6616928c16c1cb1d88f4f23.png)
for all positive integers
![n,m.](/media/m/8/4/1/841d7518147c69e1a8863801aab04e31.png)
Find the possible value for
%V0
Let $f(n)$ be a function defined on the set of all positive integers and having its values in the same set. Suppose that $f(f(n) + f(m)) = m + n$ for all positive integers $n,m.$ Find the possible value for $f(1988).$
Izvor: Međunarodna matematička olimpijada, shortlist 1988