Question 3
A function $f \colon \mathbb{N} \to \mathbb{N}$ is said to be *bonza* if $$
f(a)\quad\text{divides}\quad b^a-f(b)^{f(a)}
$$ for all positive integers $a$ and $b$.
Determine the smallest real constant $c$ such that $f(n) \leq cn$ for all bonza functions $f$ and all positive integers $n$.
f(a)\quad\text{divides}\quad b^a-f(b)^{f(a)}
$$ for all positive integers $a$ and $b$.
Determine the smallest real constant $c$ such that $f(n) \leq cn$ for all bonza functions $f$ and all positive integers $n$.