Timeline for Can a positive binary quadratic form represent 14 consecutive numbers?
Current License: CC BY-SA 3.0
23 events
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| Mar 25, 2019 at 13:10 | review | Close votes | |||
| Mar 25, 2019 at 23:04 | |||||
| Apr 13, 2017 at 12:58 | history | edited | CommunityBot |
replaced http://mathoverflow.net/ with https://mathoverflow.net/
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| S Oct 29, 2013 at 12:00 | history | suggested | Abhimanyu Pallavi Sudhir | CC BY-SA 3.0 |
[1]: http://oeis.orgA000926
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| Oct 29, 2013 at 11:38 | review | Suggested edits | |||
| S Oct 29, 2013 at 12:00 | |||||
| Aug 21, 2013 at 18:57 | vote | accept | Will Jagy | ||
| Aug 21, 2013 at 3:54 | answer | added | Lucia | timeline score: 4 | |
| Jul 31, 2010 at 0:07 | answer | added | user631 | timeline score: 22 | |
| Jun 23, 2010 at 20:53 | comment | added | David E Speyer | Your question inspired this one mathoverflow.net/questions/29280/…. | |
| Jun 18, 2010 at 5:41 | answer | added | Will Jagy | timeline score: 8 | |
| Jun 18, 2010 at 5:08 | comment | added | Pete L. Clark | @Will: Your latest edit is very interesting, but somewhat hidden at the bottom of a long list of edits. Please consider leaving it as an answer. | |
| Jun 18, 2010 at 4:46 | comment | added | Will Jagy | Note: those elements in Sloane's sequence that are $ $7 \pmod 8$ | |
| Jun 18, 2010 at 4:37 | history | edited | Will Jagy | CC BY-SA 2.5 |
added 786 characters in body
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| May 17, 2010 at 8:17 | comment | added | supercooldave | I wonder why you don't start with $f(x,y)=ax^2+bxy+cy^2+d$. Then you can set up equations $f(x,y)=0, ~f(x,y)=1, \ldots, ~f(x,y)=13$. Or perhaps this approach is too naive. | |
| May 16, 2010 at 2:46 | history | edited | Will Jagy | CC BY-SA 2.5 |
string of 10, also title to 14
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| May 12, 2010 at 3:08 | comment | added | David Hansen | ugh, you are right - i've retracted my comments. | |
| May 12, 2010 at 3:05 | comment | added | Victor Protsak | Will, these are impressive examples of long strings, but why are there two Mondays this week? :) | |
| May 12, 2010 at 3:02 | comment | added | Victor Protsak | @David: This is wrong, for each fixed positively definite form the length is bounded, see fedja's answer to the question quoted by Will as a motivation. Will's point was, in fact, that it's tricky to think of the representability of consecutive numbers as independent events. | |
| May 11, 2010 at 21:57 | history | edited | Will Jagy | CC BY-SA 2.5 |
string of 9
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| May 10, 2010 at 18:10 | history | edited | Will Jagy | CC BY-SA 2.5 |
triples, quintuples
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| May 9, 2010 at 16:25 | comment | added | Will Jagy | Yes, Victor. That applies to four or more variables, and the related 290 result allowing non-integral matrix is now proved. Density for positive binaries is 0 in the long run: if $B(n)$ is the count of integers from 1 to $n$ that are representable by $x^2 + y^2,$ then there is a constant $C = 0.7642...$ such that $ B(n) \sim C n / \sqrt{\log n} .$ So there is some reason to suspect, for any individual form, that large represented values are isolated or nearly isolated. Less predictable is the possibility of some new discriminant doing much better than smaller ones. | |
| May 9, 2010 at 7:32 | comment | added | Victor Protsak | This is reminscent of Conway's "15 theorem": if a positive definite quadratic form with integral matrix represents 1,2,...,15 then it represents all positive integers | |
| May 8, 2010 at 19:44 | comment | added | Pete L. Clark | Neat question. Why 13, exactly? | |
| May 8, 2010 at 17:48 | history | asked | Will Jagy | CC BY-SA 2.5 |