For indefinite anisotropic quadratic forms in three variables with td(f) square-free, once a single integer solution exists, there are infinitely many solutions with one coordinate having at most 6 prime factors (5 under Selberg's conjecture).
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Anisotropic quadratic equations in three variables
For indefinite anisotropic quadratic forms in three variables with td(f) square-free, once a single integer solution exists, there are infinitely many solutions with one coordinate having at most 6 prime factors (5 under Selberg's conjecture).