## Task A-4.5.

Determine all functions $f: \mathbb{N} \rightarrow \mathbb{N}$ such that for all $a, b \in \mathbb{N}$ for which $f(a) \neq b$, the following holds:

$$
f(a)-b \mid f(a)^{2}+2 b+1-f(b)^{2}
$$