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diophantine system x^2 = yz + 1 , y^2 = zx + 1, z^2 = xy + 1

Source: 2022 Czech-Polish-Slovak Match Junior, individual p2 CPSJ

September 3, 2022

number theorydiophantineDiophantine Equations

Problem Statement

Solve the following system of equations in integer numbers:

\begin{cases} x^2 = yz + 1 \\ y^2 = zx + 1 \\ z^2 = xy + 1 \end{cases}