CONO-SUR 2016 Problem 4

Let $S(n)$ be the sum of the digits of the positive integer $n$ . Find all $n$ such that $S(n)(S(n)-1)=n-1$ .

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.