Timeline for What is the smallest positive integer for which the congruent number problem is unsolved?
Current License: CC BY-SA 3.0
9 events
| when toggle format | what | by | license | comment | |
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| May 20, 2016 at 15:00 | answer | added | Kevin Buzzard | timeline score: 9 | |
| May 20, 2016 at 12:50 | answer | added | Jeremy Rouse | timeline score: 6 | |
| May 20, 2016 at 12:25 | history | edited | YCor |
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| May 20, 2016 at 11:13 | comment | added | Kevin Buzzard | Nope, I've done $10^6+1$: mwrank reports that there's a point of infinite order. Now on to $10^6+2$! This is exactly what I didn't want to do. There will surely be a smallest $N$ for which someone tried and got stuck... | |
| May 20, 2016 at 10:58 | comment | added | Kevin Buzzard | Of course, giving a talk entitled "The determination of the congruent numbers less than 10^6 and explicit 4-descents on elliptic curves" does not definitely imply that you've done what it says in the title :-) I have emailed Matsuno. | |
| May 20, 2016 at 10:54 | comment | added | Kevin Buzzard | Many thanks for this -- this is a great start. So if we believe Matsuno then $10^6+1$ is a candidate! According to pari this has analytic rank 2. Is it provably a congruent number? magma seems to say that the algebraic rank is at least 1. Does this mean it's spotted a rational point? | |
| May 20, 2016 at 10:35 | comment | added | post.as.a.guest | Then Matsuno gave a seminar talk up to $10^6$ in 2006 using 4-descent. Probably Tom Fisher could hold the "record", if he bothered with the problem. nakano.math.gakushuin.ac.jp/html-files/seminar/English/… | |
| May 20, 2016 at 10:33 | comment | added | post.as.a.guest | I thought Matsuno had the largest calculations, up to 300000 in 2005. At least that's what the ANTS-X paper (which is under BSD) on the subject says. link.springer.com/content/pdf/10.1007/978-3-642-14518-6_17.pdf | |
| May 20, 2016 at 10:21 | history | asked | Kevin Buzzard | CC BY-SA 3.0 |