Question 22
Let $\mathbb{N}$ be the set of positive integers. Find all functions $f : \mathbb{N} \to \mathbb{N}$ that satisfy the equation
$$
f^{abc-a}(abc) + f^{abc-b}(abc) + f^{abc-c}(abc) = a + b + c
$$
for all $a, b, c \ge 2$.
(Here $f^1(n) = f(n)$ and $f^k(n) = f(f^{k-1}(n))$ for every integer $k$ greater than 1.)
$$
f^{abc-a}(abc) + f^{abc-b}(abc) + f^{abc-c}(abc) = a + b + c
$$
for all $a, b, c \ge 2$.
(Here $f^1(n) = f(n)$ and $f^k(n) = f(f^{k-1}(n))$ for every integer $k$ greater than 1.)