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arXiv · 1610.06448

The generalized Catalan equation in positive characteristic

Peter Koymans
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Abstract

Let $K = \mathbb{F}_p(z_1, \ldots, z_r)$ be a finitely generated field over $\mathbb{F}_p$. In this article we study the generalized Catalan equation $ax^m + by^n = 1$ in $x, y \in K$ and integers $m, n > 1$ coprime with $p$. Our main result shows that there are only finitely many solutions up to the action of Frobenius.

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Peter Koymans. 2016-10-20. The generalized Catalan equation in positive characteristic. https://arxiv.org/abs/1610.06448

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