VMO 2005 Problem 5

Find all triples of natural $(x,y,n)$ satisfying the condition: $\frac {x! + y!}{n!} = 3^n$

Define $0! = 1$

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.