KURSCHAK 1983 Problem 1

Let $x, y$ and $z$ be rational numbers satisfying $x^3 + 3y^3 + 9z^3 - 9xyz = 0.$ Prove that $x = y = z = 0$ .

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.