IMO Shortlist 1982 problem 1


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April 2, 2012
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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).
Source: Međunarodna matematička olimpijada, shortlist 1982