Abstract: My talk is based on the work of Amit Ghosh and Peter Sarnak. For integers k, they consider the affine cubic surface given by the equation x^2+y^2+z^2-xyz=k, called the Markoff equation. They show that there are infinitely many k's for which the Hasse principle fails. This means, the equation has solutions in p-adic integers, but no solutions in integers. I will also talk about the Markoff type surface x^2+y^2+z^2-2xyz=k, which we are currently investigating.
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