Timeline for Re: Mordell's equation $y^2 = x^3 + k$ and perfect numbers
Current License: CC BY-SA 2.5
7 events
| when toggle format | what | by | license | comment | |
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| Sep 30 at 9:02 | comment | added | Jose Arnaldo Bebita | @SylvainJULIEN: Apologies for the delayed revert. But my recent preliminary computations suggest that we can take $K=k+1$. I am still working out the details. Will let you know. | |
| Apr 5, 2015 at 19:11 | comment | added | Sylvain JULIEN | @Arnie: if you ever need some non trivial consequence of BSD conjecture in your research, you might be interested in mathoverflow.net/questions/149815/… where I give a few ideas about the weak version thereof (equality of the two kinds of ranks). Hope it helps. | |
| Jun 12, 2011 at 21:28 | comment | added | Jose Arnaldo Bebita | Thanks Noam! Any references in the literature for that? (My apologies, I am still in the process of self-studying elliptic curve theory...) | |
| Jun 10, 2011 at 2:39 | comment | added | Noam D. Elkies | You might as well also assume that $k \not\equiv 0 \bmod 27$, because the curves $y^2 = x^3 + k$ and $y^2=x^3−3^{-3}k$ are isogenous and thus have the same rank. | |
| Dec 4, 2010 at 4:08 | comment | added | Jose Arnaldo Bebita | @Felipe, thanks a lot! On a side note, BSD is one of the "deepest" conjectures in number theory (i.e. Millenium Problem) but I am actually working on something which is somewhat "unrelated" -- and it's the OPN conjecture. | |
| Dec 3, 2010 at 20:11 | vote | accept | Jose Arnaldo Bebita | ||
| Dec 3, 2010 at 20:04 | history | answered | Felipe Voloch | CC BY-SA 2.5 |