Consider those functions
![f: \mathbb{N} \mapsto \mathbb{N}](/media/m/0/6/4/064f5e79a7f8bd81b5e7163e70e87d6b.png)
which satisfy the condition
for all
![m,n \in \mathbb{N}.](/media/m/d/e/2/de2c8d92fff78a13cd5c5e0fae337691.png)
Find all possible values of
Author: unknown author, Bulgaria
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Consider those functions $f: \mathbb{N} \mapsto \mathbb{N}$ 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 $f(2007).$
Author: unknown author, Bulgaria