Timeline for A binomial sum is divisible by p^2
Current License: CC BY-SA 2.5
14 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jun 8, 2010 at 13:19 | comment | added | Wadim Zudilin | The world of supercongruences is really nice and unpredictable. Some of them are easy and some are too hard. The really beautiful congruence is the one for $$ \sum_{k=1}^{(p-1)/2}\frac{(-1)^k}{k^2}\binom{2k}{k}; $$ the binomial sum is very similar to yours. Check with math/0906.5150 (the end of the preprint) on how it is related to Apery's formula for $\zeta(3)$ (more precisely to its generalization). | |
| Jan 11, 2010 at 13:48 | vote | accept | darij grinberg | ||
| Jan 11, 2010 at 5:24 | answer | added | Michael Lugo | timeline score: 4 | |
| Jan 11, 2010 at 3:53 | answer | added | dke | timeline score: 18 | |
| Jan 11, 2010 at 2:46 | answer | added | Mariano Suárez-Álvarez | timeline score: 1 | |
| Jan 10, 2010 at 18:40 | comment | added | Kevin O'Bryant | For p<2001, v_p(sum) \geq 2 if and only if p is a prime greater than 3, in which case v_p(sum) = 2. | |
| Jan 10, 2010 at 17:19 | comment | added | darij grinberg | "Almost" is good. | |
| Jan 10, 2010 at 17:18 | comment | added | john mangual | These are almost the Catalan numbers. | |
| Jan 10, 2010 at 16:34 | comment | added | darij grinberg | I have done it 1 minute before you wrote your comment. Basically it was a mistake in my notes that I fixed in the text but forgot to fix it in the title. Sorry. | |
| Jan 10, 2010 at 16:30 | comment | added | Ben Weiss | I'm just wondering if you can clean up the discrepancy between the title which suggests you think the answer is 1, and the problem where you state it as 0. | |
| Jan 10, 2010 at 16:29 | history | edited | darij grinberg | CC BY-SA 2.5 |
added 44 characters in body; edited title
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| Jan 10, 2010 at 16:25 | comment | added | darij grinberg | I know of Wolstenholme's theorem - but it seems to weak to be of use here. | |
| Jan 10, 2010 at 16:10 | comment | added | Steve Huntsman | This might help: mathworld.wolfram.com/WolstenholmesTheorem.html | |
| Jan 10, 2010 at 15:40 | history | asked | darij grinberg | CC BY-SA 2.5 |