# Are you smarter than me?

Algebra Level 5

Find the number of solutions $$\left(x,y,z\right)$$ to the system of equations

\begin{align} x+2y+4z&=9\\ 4yz+2zx+xy&=13\\ xyz&=13 \end{align}

such that at least two of $$x,y,z$$ are integers.

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