IMO Shortlist 1982 problem 1
Dodao/la:
arhiva2. travnja 2012. The function
![f(n)](/media/m/d/3/e/d3e47283bffbbf24c97f0c6474d5a82d.png)
is defined on the positive integers and takes non-negative integer values.
![f(2)=0,f(3)>0,f(9999)=3333](/media/m/d/9/3/d933f5c3c2c4f45e1784ab539203af96.png)
and for all
![f(m+n)-f(m)-f(n)=0 \text{ or } 1.](/media/m/7/8/0/7809801d9e816d309dde366d9a24c4ad.png)
Determine
![f(1982)](/media/m/8/b/7/8b7a7ba50e6971e7836a6caa63706bef.png)
.
%V0
The function $f(n)$ is defined on the positive integers and takes non-negative integer values. $f(2)=0,f(3)>0,f(9999)=3333$ and for all $m,n:$ $$f(m+n)-f(m)-f(n)=0 \text{ or } 1.$$ Determine $f(1982)$.
Izvor: Međunarodna matematička olimpijada, shortlist 1982