Competition problem — Number theory

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Number theory Difficulty 5.6 AIME, harder Find the answer

[23.1] Let $f(n)$ be a function defined on the set of positive integers, with values in the set of non-negative integers, and satisfying:
(i) $f(2)=0, f(3)>0, f(9999)=3333$ ;
(ii) For any $m, n$ , $f(m+n)-f(m)-f(n)=0$ or 1. Find $f(1982)$ .

Your answer

A number or a short expression. Fractions can be typed as 3/2, and spacing doesn't matter.

Solution

None

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None

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Source: NuminaMath-1.5, licensed Apache-2.0. Statement and solution reproduced as published; topic and difficulty added by this site.