OMCPLP 2022 Problem 1

How many triples $(a,b,c)$ with $a,b,c \in \mathbb{R}$ satisfy the following system? $\begin{cases} a^4-b^4=c b^4-c^4=a c^4-a^4=b \end{cases}$ .

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.