# Prime Again?

Number Theory Level 4

$\large{\begin{cases} x^2 + xy + y^2 &=& 19 \\ y^2 + yz + z^2 &=& 67 \\ z^2 + zx + x^2 &=& 79 \\ \end{cases} }$

Considering the system of Diophantine equations above, what is the value of $$xy + yz +zx$$ ?

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