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arxiv: math/0507405 · v1 · submitted 2005-07-20 · 🧮 math.AG · math.CV

Integer points on a curve and the plane Jacobian problem

classification 🧮 math.AG math.CV
keywords integercurvejacobianplanepointspolynomialcoefficientscomplex
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A polynomial map $F=(P,Q)\in \Z [x,y]^2$ with Jacobian $JF:=P_xQ_y-P_yQ_x\equiv 1$ has a polynomial inverse of integer coefficients if the complex plane curve P=0 has infinitely many integer points.

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