does Oppenheim conjecture hold for specific quadratic forms? or for generic quadratic forms with a set of measure 1. 


for example can we find $x,y,z \in \mathbb{Z}$ with
$$|x^2 + y^2 - \sqrt{3} z^2| < 10^{-6}$$
is that implied by Oppenheim conjecture?


where are elementary expositions of proof? what is the current standing?? I know the proof involves homogeneous flows




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is Wikipedia correct here? I thought it was almost all indefinite ternary quadratic forms $ax^2 + by^2 - cz^2$ with $[ a:b:c]$ not all rational.


Wikipedia is known to have dubious statements. here I am wondering what orbit(s) were used with Ratner theorem or any elementary proof that $10^{-100}$ is possible. 



Find $x,y,z \in \mathbb{Z}$ with $|x^2 + y^2 - \sqrt{3} z^2| < 10^{-6}$
$x=6627,y=314048,z=238678$ is an answer to the question in the title but I'm sure that the real question is something I don't really understand.


