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On power values of binary forms over function fields. (English) Zbl 0880.11032

Let \(K\) be an algebraic function field and let \(F\in K[X,Y]\) be a binary form of degree \(n\) with distinct roots. The author proves that for \(n\geq 5\) all solutions of \[ F(X,Y)=z^m \quad x,y,z\in K,\;m\in\mathbb{Z} \] satisfy \[ H_K\left(\frac{x}{y}\right)\leq 10H_K(z)+C, \] where the effectively computable constant depends only on \(F\) and \(K\).
Reviewer: I.Gaál (Debrecen)

MSC:

11D61 Exponential Diophantine equations
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