BALKAN 1984 Problem 4

Let $a,b,c$ be positive real numbers. Find all real solutions $(x,y,z)$ of the system: $ax+by=(x-y)^{2} by+cz=(y-z)^{2} cz+ax=(z-x)^{2}$

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.