MathLabs

Problem 1

The function f(n)f(n) is defined on the positive integers and takes non-negative integer values. f(2)=0f(2)=0, f(3)>0f(3)>0, f(9999)=3333f(9999)=3333, and for all m,nm,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).
Step 4 of 7: Evaluate f(1980)f(1980)
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In plain words

A direct instance of the general formula just proved.

f(1980)=f(3⋅660)=660f(1980)=f(3\cdot660)=660
Detailed analysis

Since 660≤3333660\le3333, Step 3 applies directly with k=660k=660.