UA-UMO 1999 Problem 96

Find all pairs $(k,l)$ of positive integers such that $\frac{k^l}{l^k}=\frac{k!}{l!}$ .

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.