DE-MO 1997 Problem 4

Find all real solutions $(x,y,z)$ of the system of equations $\begin{cases} x^3 = 2y-1 y^3 = 2z-1 z^3 = 2x-1\end{cases}$

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.