olymmath

IMO 1982 Problem 1

  • Day 1

The function f(n)f(n) is defined on the positive integers and takes non-negative integer values. f(2)=0,f(3)>0,f(9999)=3333f(2)=0,f(3)>0,f(9999)=3333 and for all m,n:m,n: f(m+n)−f(m)−f(n)=0 or 1.f(m+n)-f(m)-f(n)=0 \text{ or } 1. Determine f(1982)f(1982) .

Dataset text AI-MO AoPS. Quoted with source.

Official text: IMO 1982 official English paper, page 1.

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