IL-GILLIS 2023 Problem 4

For each positive integer $n$ , find all triples $a,b,c$ of real numbers for which $\begin{cases}a=b^n+c^n b=c^n+a^n c=a^n+b^n\end{cases}$

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.