Question 2
Consider those functions $f: \mathbb{N} \rightarrow \mathbb{N}$ which satisfy the condition
$$
f(m+n) \geq f(m)+f(f(n))-1
$$
for all $m, n \in \mathbb{N}$. Find all possible values of $f(2007)$.
($\mathbb{N}$ denotes the set of all positive integers.)
$$
f(m+n) \geq f(m)+f(f(n))-1
$$
for all $m, n \in \mathbb{N}$. Find all possible values of $f(2007)$.
($\mathbb{N}$ denotes the set of all positive integers.)