Timeline for On the solutions of $f(x) = y^k$ with $f \in \mathbb{Z}[x]$, $k \in \mathbb{N}$
Current License: CC BY-SA 3.0
5 events
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| Apr 17, 2017 at 9:58 | comment | added | trenta3 | Thanks for answering what I supposed to be the original question. I've changed the question by only allowing $k \ge 3$ and I'm interested in the whole set of solutions (for any $k$). I know that theorem of Siegel, but it doesn't say anything if you allow $k$ to vary and consider all such solutions. Sorry for mistating the question. | |
| Apr 17, 2017 at 7:41 | comment | added | Peter Mueller | @AntonFetisov You are right, I misread the question, which as asked of course is nonsense. | |
| Apr 17, 2017 at 1:15 | comment | added | Anton Fetisov | The line $y \in \mathbb Z[x]$ in op's question makes me think he's asking not about points on curves, but about the roots in the polynomial ring. | |
| Apr 16, 2017 at 22:57 | comment | added | KConrad | @W.Schlieper are you confusing integral points and rational points? The number of integral points is finite by Siegel's theorem, even for genus 1. | |
| Apr 16, 2017 at 22:48 | history | answered | Peter Mueller | CC BY-SA 3.0 |