Question 35
Find all functions $f : \mathbb{N} \to \mathbb{N}$ such that for all positive integers $a, b$ we have
$$
f^a(b) + f^b(a) \mid 2(f(ab) + b^2 - 1).
$$
By $f^a(x)$ we mean the $a$-fold composition of $f$.
$$
f^a(b) + f^b(a) \mid 2(f(ab) + b^2 - 1).
$$
By $f^a(x)$ we mean the $a$-fold composition of $f$.