Question 50
Find all the functions $f : \mathbb{N} \to \mathbb{N}$ such that for $x, y \in \mathbb{N}$:
$$
0 \le y + f(x) - f^{f(y)}(x) \le 1
$$
where
$$
f^n(x) = \underbrace{f(f(\cdots(f(x))\cdots))}_{n}
$$
$$
0 \le y + f(x) - f^{f(y)}(x) \le 1
$$
where
$$
f^n(x) = \underbrace{f(f(\cdots(f(x))\cdots))}_{n}
$$