Timeline for Perfect powers on genus 0 curves (with restrictions)
Current License: CC BY-SA 3.0
11 events
| when toggle format | what | by | license | comment | |
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| Aug 27, 2013 at 15:26 | history | bounty ended | CommunityBot | ||
| Aug 25, 2013 at 6:03 | comment | added | joro | It is more clear to me after the remarks, thanks. | |
| Aug 24, 2013 at 22:21 | history | edited | Peter Mueller | CC BY-SA 3.0 |
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| Aug 23, 2013 at 12:53 | comment | added | Peter Mueller | @joro: I guess a CAS might return a negative genus if the curve is not absolutely irreducible. If the curve nevertheless is irreducible, then there are only finitely many points on it. So when reducing to irreducible, you in addition may assume that the curve is absolutely irreducible. | |
| Aug 23, 2013 at 11:32 | comment | added | joro | I suppose you assume genus 0 of the curve? What about curves for which CASes return negative genus (maybe singular and others) yet the curves have infinitely many integral points? | |
| Aug 20, 2013 at 9:13 | comment | added | Peter Mueller | Well, but this curve contains a straight line. Trivial examples like this are always possible. However, as your function $\text{High}$ is multiplicative, your question only makes sense for irreducible polynomials. | |
| Aug 20, 2013 at 8:21 | comment | added | joro | Hm, isn't $x^n-y^n=0$ counterexample to your claim about degree 2?. Points are (t,t). High(x^n-y^n)=x^n-y^n, the degree is n and it is squarefree? | |
| Aug 20, 2013 at 7:57 | comment | added | Peter Mueller | @joro: Indeed, it doesn't seem to be necessary to use these additional assumptions in order to reduce to degree $2$ which is easy to handle. | |
| Aug 20, 2013 at 6:59 | comment | added | joro | You don't mention coprimality at all. You don't need it to answer the question? | |
| Aug 20, 2013 at 6:32 | comment | added | joro | You don't use the hypothesis about perfect powers and in particular $m \ge 3$? You don't need this hypothesis to answer the question? | |
| Aug 19, 2013 at 19:28 | history | answered | Peter Mueller | CC BY-SA 3.0 |