How many functions $f : \{1, 2, . . . , 16\} \to \{1, 2, . . . , 16\}$ have the property that $f(f(x))-4x$ is divisible by $17$ for all integers $1 \le x \le 16$?
Problem
Source: 2021 Dürer Math Competition Finals Day2 E14 https://artofproblemsolving.com/community/c2749870_
Tags: number theory, divisible, divides