Prime, Prime, Prime

Algebra Level 4

{a2+bc=67b2+ac=71c2+ab=79\begin{cases} a^2 + bc = 67\\ b^2 + ac = 71\\ c^2 + ab = 79 \end{cases}

Considering the equations above with integers a,b,ca, b, c, what is the value of ab+bc+caab + bc + ca?

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