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Jun 8, 2017 at 0:17 comment added P. Koymans My main intention was to reprove the Beukers and Schlickewei result using the height bound as stated in the question. Such a proof would have the additional advantage that it works in characteristic $p$ if one makes the obvious restriction that $x, y \not \in G^p$.
Jun 7, 2017 at 18:01 history answered Felipe Voloch CC BY-SA 3.0