RU-ALLRUSSIAN 2023 Problem 105

Find the largest natural number $n$ for which the product of the numbers $n, n+1, n+2, \ldots, n+20$ is divisible by the square of one of them.

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.