Question 30
Let $\mathbb{Z}_{ \gt 0}$ denote the set of positive integers. A function $f\colon \mathbb{Z}_{ \gt 0} \to \mathbb{Z}_{ \gt 0}$ is said to be bonza if
$$ f(a)\ \mid\ b^{a}-f(b)^{f(a)} $$
for all positive integers $ a $ and $ b $.
Determine the smallest constant c such that $ f(n) \leq cn $ for any bonza function f and any positive integer n.
$$ f(a)\ \mid\ b^{a}-f(b)^{f(a)} $$
for all positive integers $ a $ and $ b $.
Determine the smallest constant c such that $ f(n) \leq cn $ for any bonza function f and any positive integer n.