Timeline for Is there an elementary way to find the integer solutions to $x^2-y^3=1$?
Current License: CC BY-SA 2.5
16 events
| when toggle format | what | by | license | comment | |
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| Feb 8, 2021 at 3:52 | history | protected | CommunityBot | ||
| Sep 10, 2013 at 10:37 | history | edited | user9072 |
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| Jul 13, 2011 at 17:35 | answer | added | Franz Lemmermeyer | timeline score: 18 | |
| May 31, 2011 at 14:46 | vote | accept | Pace Nielsen | ||
| May 27, 2011 at 1:32 | answer | added | paul Monsky | timeline score: 28 | |
| Sep 22, 2010 at 16:55 | comment | added | Robin Chapman | Schoof's book reprints Euler's argument in the original Latin :-) | |
| Sep 22, 2010 at 15:55 | comment | added | Pace Nielsen | Thank you James and Franz. I'll take a look at those sources. | |
| Sep 22, 2010 at 6:00 | comment | added | Franz Lemmermeyer | I sketched Euler's proof in "A note on Pépin's counter examples to the Hasse principle for curves of genus 1", which you can find online. | |
| Sep 22, 2010 at 1:30 | answer | added | Gerry Myerson | timeline score: 4 | |
| Sep 22, 2010 at 1:16 | comment | added | user2490 | You can find a discussion of two approaches to this problem in Schoof's "Catalan's Conjecture." An appendix to the book describes Euler's original approach (the reference for which Schoof includes), and Chapter 4 of the book describes an alternative approach due to William McCallum. | |
| Sep 22, 2010 at 1:07 | history | edited | Gjergji Zaimi |
removed tag "algebraic", added "elementary"
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| Sep 22, 2010 at 0:54 | answer | added | Gjergji Zaimi | timeline score: 19 | |
| Sep 22, 2010 at 0:54 | history | edited | Charles |
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| Sep 22, 2010 at 0:25 | comment | added | James Weigandt | Building on Cam McLeman's comment, this elliptic curve has a point of order 6, and hence possesses a 2-isogeny. A descent via 2-isogeny shouldn't be too hard to write out explicitly. It would be interesting (but perhaps not what Pace Nielsen is going for) if someone could give an elementary classification of the rational points on this curve based on the fact that it is the modular curve $X_0(36)$. | |
| Sep 22, 2010 at 0:07 | comment | added | Cam McLeman | Elementary includes avoiding elliptic curves? Because there are not-so-hard arguments with the basic theory set up. | |
| Sep 22, 2010 at 0:04 | history | asked | Pace Nielsen | CC BY-SA 2.5 |