Timeline for Is the following consequence of the Lang conjecture known?
Current License: CC BY-SA 3.0
16 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Mar 13, 2015 at 18:09 | vote | accept | R.P. | ||
| Mar 13, 2015 at 22:41 | |||||
| Oct 12, 2014 at 19:51 | comment | added | Michael Stoll | Stating the obvious: the mere existence of a function $f$ is trivial, just take $f(n)$ to be the (finite) number of solutions... | |
| Jan 28, 2014 at 14:57 | comment | added | GH from MO | @joro: I see, then René has answered your question. | |
| Jan 28, 2014 at 14:48 | comment | added | joro | @GHfromMO Thanks. I asked about the largest number of solutions known. | |
| Jan 28, 2014 at 14:46 | comment | added | GH from MO | @René: I think joro asked what is known with proof. | |
| Jan 28, 2014 at 14:46 | comment | added | GH from MO | @joro: I don't know what is the best current bound on $f(n)$. | |
| Jan 28, 2014 at 11:17 | comment | added | R.P. | Euler noticed that $59^4+158^4=133^4+134^4$. This already gives $16$ solutions to $x^4+y^4=n$, where $n=635318657$ (apply the symmetries $(x,y)\mapsto(\pm x,\pm y)$ and $(x,y)\mapsto(y,x)$). According to Hardy and Wright then, this must be conjectured as being the record number of solutions for any $n$. | |
| Jan 28, 2014 at 5:49 | comment | added | joro | @GHfromMO what is the current record for number of solutions? | |
| Jan 27, 2014 at 23:12 | history | edited | R.P. | CC BY-SA 3.0 |
deleted 2 characters in body
|
| Jan 27, 2014 at 23:03 | history | edited | R.P. | CC BY-SA 3.0 |
added 101 characters in body
|
| Jan 27, 2014 at 19:09 | comment | added | GH from MO | We certainly have $f(n)\ll_\epsilon n^\epsilon$ for any $\epsilon>0$, and we should have $f(n)\leq 16$ but this is widely open. See my comments to ACL's response. | |
| Jan 27, 2014 at 19:05 | comment | added | Qiaochu Yuan | Your question is stated slightly confusingly - your friend asks for a bound depending on $n$ but you ask for a bound independent of $n$, and perhaps this is what confused ACL. | |
| Jan 27, 2014 at 15:50 | vote | accept | R.P. | ||
| Jan 27, 2014 at 16:12 | |||||
| Jan 27, 2014 at 15:46 | answer | added | ACL | timeline score: 6 | |
| Jan 27, 2014 at 15:45 | history | edited | R.P. | CC BY-SA 3.0 |
in description of the main question, x,y should be integers
|
| Jan 27, 2014 at 15:35 | history | asked | R.P. | CC BY-SA 3.0 |