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Abstract:
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This thesis consists of three chapters . Chapter 1 explains how the research problems considered in this thesis fit into the investigation of local -global principle in the diophantine geometry , as well as gives a unified sketch of the proofs of the two main results in this thesis . Chapter 2 establishes a similar conclusion to Theorem B of a paper by Poonen and Voloch in another settings . Chapter 3 relates to the object considered in the main result of Chapter 2 to an old conjecture proposed by Skolem and solves some cases of its analog . |