Timeline for Equation $x^2=y^p + 1$
Current License: CC BY-SA 3.0
8 events
| when toggle format | what | by | license | comment | |
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| Nov 14, 2015 at 12:39 | comment | added | Fedor Petrov | @WadimZudilin many thanks! Now I see from your notes, that Nagell's result is immediate after using Pell equation. | |
| Nov 14, 2015 at 12:17 | comment | added | Wadim Zudilin | Fedor, this divisibility result is in the heart of the resolution of Catalan's problem by Preda Mihăilescu, not just of this particular case. It is in Mordell's book but I also have all the related things recorded in Russian (wain.mi.ras.ru/cp) after our 2001-02 Moscow seminar. The notes ("Elementary introduction") includes Euler's proof, Nagell's results and proofs from both Ko Chao and Chein. It is a fascinating story! | |
| Nov 14, 2015 at 11:46 | comment | added | Fedor Petrov | @WadimZudilin Chein's paper cites Nagell's previous result that $p$ divides $y+1$, I can't neither find Nagell's paper online nor prove it myself, would you please explain this? | |
| Nov 14, 2015 at 1:40 | comment | added | Todd Trimble | @paulgarrett Perhaps the downvote was reversed; right now none is there. | |
| Nov 14, 2015 at 0:59 | comment | added | paul garrett | I don't understand the down-vote to the question, really: if we ignore the specifics, and "make it a better question than it is", it asks about higher-genus curves, Mordell-Weil, ABC-conjecture, and such, I think, ... | |
| Nov 14, 2015 at 0:04 | comment | added | GH from MO | I fixed the date of Ko Chao's publication (Sci. Sinica (Notes) 14 (1964), 457-460). | |
| Nov 14, 2015 at 0:03 | history | edited | GH from MO | CC BY-SA 3.0 |
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| Nov 13, 2015 at 23:35 | history | answered | Wadim Zudilin | CC BY-SA 3.0 |