Find all triples (x,y,z) of integers which satisfy
x(y \plus{} z) \equal{} y^2 \plus{} z^2 \minus{} 2
y(z \plus{} x) \equal{} z^2 \plus{} x^2 \minus{} 2
z(x \plus{} y) \equal{} x^2 \plus{} y^2 \minus{} 2. symmetrygeometryinequalitiesnumber theory proposednumber theory