Timeline for Prefix sums of Pascal triangle = powers of two
Current License: CC BY-SA 3.0
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| Oct 21, 2017 at 16:02 | history | edited | Aaron Meyerowitz | CC BY-SA 3.0 |
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| Oct 21, 2017 at 6:22 | history | edited | Aaron Meyerowitz | CC BY-SA 3.0 |
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| Oct 21, 2017 at 3:30 | comment | added | Noam D. Elkies | There's also $S_{90,2} = 2^{12}$, though it's known that there's no perfect binary $[90,78,5]$ code. The theorem of Tietäväinen and van Lint does not require a complete solution of $S_{n,m} = 2^k$ (and the corresponding equation for other prime-power values of the alphabet size $k$); as far as I know it is still an open question whether there are any other cases where $S_{n,m}$ is a power of two (the $m=2$ case is equivalent to the celebrated Ramanujan-Nagell theorem). | |
| Oct 21, 2017 at 2:40 | history | answered | Aaron Meyerowitz | CC BY-SA 3.0 |