Integral points on Markoff type cubic surfaces

Amit Ghosh, Peter Sarnak

For integers $k$, we consider the affine cubic surface $V_k$ given by $M(\mathbf{x})=x_1^2+x_2^2+x_3^2-x_1{x}_2{x}_3=k$. We show that for almost all $k$ the Hasse Princi…