Question 56
Find all functions $f: \mathbb{N} \rightarrow \mathbb{N}$ such that for all positive integers $n$
i. $f(n) \lt f(n + 1) \lt f(n) + 2020$;
ii. $S(f(n)) = f(S(n))$.
(Where $S(n)$ is the sum of digits of $n$ in base 10.)
i. $f(n) \lt f(n + 1) \lt f(n) + 2020$;
ii. $S(f(n)) = f(S(n))$.
(Where $S(n)$ is the sum of digits of $n$ in base 10.)