Timeline for binomial/factorial identity mod p
Current License: CC BY-SA 3.0
9 events
| when toggle format | what | by | license | comment | |
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| Jul 2, 2015 at 15:38 | answer | added | Salvo Tringali | timeline score: 0 | |
| Jul 2, 2015 at 2:00 | comment | added | David Handelman | Right, Lucas' theorem yields it immediately. The proof below is good, too. Thanks everyone. | |
| Jul 2, 2015 at 1:56 | vote | accept | David Handelman | ||
| Jul 2, 2015 at 1:35 | answer | added | Lev Borisov | timeline score: 6 | |
| Jul 2, 2015 at 1:28 | comment | added | Benjamin Steinberg | If p^a divides M, this is easy. Just let C_M be the cyclic group of order M and let G be the p^a element subgroup. Then G acts on the p^a element subsets if C_M and the fixed points of G are its cosets. So it follows from the fact that the number of fixed points of a p-group acting on a set is congruent to the size of the set mod p. I don't know if this idea can be adapted to the general case. | |
| Jul 2, 2015 at 1:25 | comment | added | Gerhard Paseman | Do you know of Kummer's theorem (or Lucas's theorem) on binomial coefficients? I think it would be a consequence of one of those. Gerhard "Don't Have A Literature Reference" Paseman, 2015.07.01 | |
| Jul 2, 2015 at 1:24 | comment | added | Mayank Pandey | See Lucas's Theorem. | |
| Jul 2, 2015 at 1:20 | history | edited | David Handelman |
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| Jul 2, 2015 at 1:13 | history | asked | David Handelman | CC BY-SA 3.0 |