Question 6
Determine all functions $f(n)$ defined on the nonnegative integers, with values in $\{0,1,2,\ldots,2000\}$, satisfying:
(a) $f(n)=n$ for $0\le n\le2000$;
(b) $f(f(m)+f(n))=f(m+n)$ for all positive integers $m,n$.
(a) $f(n)=n$ for $0\le n\le2000$;
(b) $f(f(m)+f(n))=f(m+n)$ for all positive integers $m,n$.