DE-BUNDESWETTBEWERB 2003 Problem 2

Find all triples $\left(x,\ y,\ z\right)$ of integers satisfying the following system of equations:

$x^3-4x^2-16x+60=y$ ; $y^3-4y^2-16y+60=z$ ; $z^3-4z^2-16z+60=x$ .

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.