Problem

Source: Canada RepĂȘchage 2021/2 CMOQR

Tags: algebra, system of equations, Canada, repechage



Determine all integer solutions to the system of equations: \begin{align*} xy + yz + zx &= -4 \\ x^2 + y^2 + z^2 &= 24 \\ x^{3} + y^3 + z^3 + 3xyz &= 16 \end{align*}