Let \mathbb{N} denote the set of positive integers. A function f\colon\mathbb{N}\to\mathbb{N} is said to be bonza if
f(a)~~\text{divides}~~b^a-f(b)^{f(a)}
for all positive integers a and b.
Determine the smallest real constant c such that f(n)\leqslant cn for all bonza functions f and all positive integers n.
Proposed by Lorenzo Sarria, Colombia