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Cyclic system of equations with three variables

Source: Lusophon Mathematical Olympiad 2022 Problem 1

November 3, 2022
algebrasystem of equations

Problem Statement

How many triples (a,b,c)(a,b,c) with a,b,c∈Ra,b,c \in \mathbb{R} satisfy the following system?
{a4−b4=cb4−c4=ac4−a4=b\begin{cases} a^4-b^4=c \\ b^4-c^4=a \\ c^4-a^4=b \end{cases}.
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