CZ-SK-MO 1992 Problem 3

Let $S(n)$ denote the sum of digits of $n \in N$ . Find all $n$ such that $S(n) = S(2n) = S(3n) =... = S(n^2)$

Dataset text AI-MO AoPS. Quoted with source.

Solutions

No solution is on olymmath yet. Official and human solutions come first when they arrive. AI solutions come after them, with a label.