Timeline for What numbers are integrally represented by $4 x^2 + 2 x y + 7 y^2 - z^3$
Current License: CC BY-SA 3.0
14 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Apr 13, 2017 at 12:58 | history | edited | CommunityBot |
replaced http://mathoverflow.net/ with https://mathoverflow.net/
|
|
| Dec 4, 2012 at 23:16 | history | edited | Will Jagy |
no more asking. now we are telling.
|
|
| Aug 21, 2012 at 18:22 | comment | added | Will Jagy | @joro, yes, and a bit stronger than what you write. If $p \equiv 1 \pmod 3,$ then we have $p = u^2 + 3 v^2,$ after which we get a choice of $p = r^2 + 27 s^2$ or $p = 4 t^2 \pm 2 t w + 7 w^2,$ but not both. If $p = r^2 + 27 s^2,$ then $z^3 \equiv 2 \pmod p$ has integer solutions. If $p = 4 t^2 \pm 2 t w + 7 w^2,$ then $z^3 \equiv 2 \pmod p$ does not have integer solutions. See Ireland and Rosen, A Classical Introduction to Modern Number Theory, and David A. Cox, Primes of the Form $x^2 + n y^2.$ That is why one direction in this problem (the M.A.A. question) is not difficult. | |
| Aug 21, 2012 at 15:16 | comment | added | joro | Are there known obstructions a prime to be both $z^3 \pm 2$ and $ 4 u^2 + 2 u v + 7 v^2 $ ? | |
| Aug 20, 2012 at 19:34 | history | edited | Will Jagy | CC BY-SA 3.0 |
added 435 characters in body
|
| Aug 18, 2012 at 0:56 | history | edited | Will Jagy |
edited tags
|
|
| Aug 18, 2012 at 0:23 | comment | added | user9072 | @Will Jagy: thanks for the reply. Let me say it like this: if such tagging stays an exception I can live with it without problem. If it should however become some general trend, I'd find it anoying. One other thing: you do not have a top-level arXiv tag, like nt.number-theory, and no more space for it. I do not know how K.B. and M.E. read MO. But, if I'd not be frequently around, I'd just look at my preferred top-level tags. So, it could even be that on a practical level a standard NT-tag would help more than the personalized ones. In any case, I hope you get a good answer. Good luck! | |
| Aug 17, 2012 at 21:53 | comment | added | Will Jagy | @quid, it started by request, of a sort, at the earliest of these: mathoverflow.net/questions/tagged/ask-johnson where all involved intended it as humorous. I tried this at MSE math.stackexchange.com/questions/93600/… where some local lout deleted it without consulting me. I like your way better. I would like to give it some time before deleting them, though, perhaps a day, this question and related ones have been on my mind for several years. Kevin and Matt are now both intermittent MO participants. | |
| Aug 17, 2012 at 20:58 | comment | added | user9072 | Am I the only one that finds this use of tags strange? | |
| Aug 17, 2012 at 20:39 | history | edited | Will Jagy | CC BY-SA 3.0 |
added 9 characters in body; edited tags
|
| Aug 17, 2012 at 19:05 | history | edited | Will Jagy | CC BY-SA 3.0 |
added 1401 characters in body
|
| Aug 17, 2012 at 4:27 | history | edited | Will Jagy | CC BY-SA 3.0 |
added 246 characters in body
|
| Aug 17, 2012 at 3:38 | comment | added | Steven Gubkin | +1 for ask-kevin-buzzard | |
| Aug 17, 2012 at 3:31 | history | asked | Will Jagy | CC BY-SA 3.0 |