Question 66
Find all functions $f: \mathbb{Z}^{+} \rightarrow \mathbb{Z}^{+}$ satisfying $f(1)=2$, $f(2) \neq 4$, and
$$
\max \{f(m)+f(n), m+n\} \mid \min \{2m+2n, f(m+n)+1\}
$$
for all $m, n \in \mathbb{Z}^{+}$.
$$
\max \{f(m)+f(n), m+n\} \mid \min \{2m+2n, f(m+n)+1\}
$$
for all $m, n \in \mathbb{Z}^{+}$.