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Let ϕ : X → X be a morphism of a variety over a number field K. We consider local conditions and a " Brauer-Manin " condition, defined by Hsia and Silverman, for the orbit of a point P ∈ X(K) to be disjoint from a subvariety V ⊆ X, i.e., for O ϕ (P) ∩ V = ∅. We provide evidence that the dynamical Brauer-Manin condition is sufficient to explain the lack of… (More)

We give bounds on the number of solutions to the Diophantine equation (X+1/x)(Y +1/y) = n as n → ∞. These bounds are related to the number of solutions to congruences of the form ax+by = 1 modulo xy.

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