Integral points on plane curves and Plane Jacobian Conjecture over number fields

Abstract

Let $K$ be a number field and $O_K$ the ring of integers of $K$. In the spirit of Siegel's theorem on integral points on affine algebraic curves, the plane Jacobian conjecture over $K$ is equivalent to the following statement: if $P,Q\in O_K[x,y]$ and $P_x{Q}_y-P_y{Q}_x\equiv 1$, then the curve $P=0$ has more than one integral point.

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