Question 12
Let $\mathbb N$ be the set of all positive integers. A function $f:\mathbb N\to\mathbb N$ satisfies $f(m+n)=f(f(m)+n)$ for all $m,n\in\mathbb N$, and $f(6)=2$. Also, no two of the values $f(6),f(9),f(12),f(15)$ coincide. How many three-digit positive integers $n$ satisfy $f(n)=f(2005)$?