Timeline for Can a positive binary quadratic form represent 14 consecutive numbers?
Current License: CC BY-SA 2.5
8 events
| when toggle format | what | by | license | comment | |
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| Aug 21, 2013 at 18:57 | vote | accept | Will Jagy | ||
| Aug 21, 2013 at 12:58 | history | undeleted |
Andrés E. Caicedo François G. Dorais |
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| Aug 21, 2012 at 7:20 | history | deleted | user631 | ||
| Aug 13, 2010 at 3:46 | comment | added | Will Jagy | Powerpuff, I asked them to merge your two accounts under the registered one. I did not notice your comment until today. The intention of the software is that a comment immediately after an answer or question, but by someone else, is brought to the user's attention if they leave MO and then log back in. It does not always work anyway, I am not sure what variables affect that. So anyway, this comment and yours on August 2 are counted as comments to your post. Have you any idea how to search for seven consecutive numbers represented by all forms with $\Delta = -71$? Will. | |
| Aug 2, 2010 at 4:53 | comment | added | user631 | @Jagy, your "stronger conjecture" follows immediately from Hypotheses H by the same argument I gave --- If you think about Lemma 2, it also shows (under the same hypothesis) that for every ideal class [c] in C, there exists an ideal N_c of norm n*prod_{A_i} p_i. Correspondingly, the integers dM+k+j are represented by ALL positive forms of discriminant -q. | |
| Jul 31, 2010 at 3:36 | comment | added | Will Jagy | Just to record this, my strongest conjecture is that (for my favorite discriminants $\Delta = -q$) there is a string of $p$ consecutive integers (where $p$ is the first quadratic nonresidue $\pmod q$) that are integrally represented by ALL the positive forms of discriminant $-q.$ So, for $\Delta = -311$ we are asking for 11 numbers, for $-479$ we want 13 numbers, for $-1559$ we want 17 consecutive numbers. Note that I cannot exhibit anything even for $-71.$ But as long as I'm just making up things up, why not? | |
| Jul 31, 2010 at 2:19 | comment | added | Will Jagy | Goodness, thank you for your effort. First, please see David Speyer's mathoverflow.net/questions/29280/… If, as I suspect, you have shown that Schinzel's H implies an answer to David's question, you might put a relatively short answer there and link back to this. Next, note among my questions, we did eventually confirm that any positive binary represents arbitrarily long arithmetic progressions of primes by Green-Tao, but being primes these numbers will be very far from consecutive. Consider registering on MO! | |
| Jul 31, 2010 at 0:07 | history | answered | user631 | CC BY-SA 2.5 |