Timeline for Write {1,...,3n} as the disjoint union of arithmetic progressions of length 3 and steps 1, 2,...,n
Current License: CC BY-SA 3.0
13 events
| when toggle format | what | by | license | comment | |
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| Apr 28, 2017 at 19:48 | comment | added | Wade Hann-Caruthers | Curiously, it appears not to work for numbers that do not satisfy your assumption, suggesting you may have some obstruction for those...care to share? :) | |
| Apr 28, 2017 at 19:33 | comment | added | Wade Hann-Caruthers | I tried it for some small values (small but bigger than 2) and it is possible to do this for n = 9, 10, 11, 18, 19. 20. For 10, for example, the following works: (1, 2, 3) (4, 6, 8) (7, 10, 13) (20, 24, 28) (11, 16, 21) (17, 23, 29) (12, 19, 26) (14, 22, 30) (9, 18, 27) (5, 15, 25) | |
| Apr 27, 2017 at 3:17 | comment | added | Gerhard Paseman | Look up Langford sequences/triples. There is a variation where step size is i+1 instead of i. One of them has solutions with those values of n, and there may be a proof that those values are necessary. Gerhard "Doesn't Know The Proof Yet" Paseman, 2017.04.26. | |
| Apr 27, 2017 at 2:53 | comment | added | Gerry Myerson | @René, for small values of $n$, there are certainly no solutions. E.g., for $n=3$, $A_1$ and $A_3$ can't be disjoint. It's not immediately clear to me what happens when $n$ is large. (Although I realize $n=3$ doesn't satisfy the congruence modulo 9, but it's also not clear to me why one wants to impose that condition.) | |
| Apr 27, 2017 at 0:13 | comment | added | R.P. | Wait, so how does this work for $n=2$? | |
| Apr 27, 2017 at 0:06 | review | Close votes | |||
| Apr 27, 2017 at 12:11 | |||||
| Apr 26, 2017 at 23:31 | history | edited | Gerry Myerson | CC BY-SA 3.0 |
added 24 characters in body
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| Apr 26, 2017 at 23:29 | comment | added | Gerry Myerson | I'm not sure whether this is the right forum or not, but I would like to know the source of this question, and what you have found in your own efforts to solve it, William. | |
| Apr 26, 2017 at 23:11 | review | Low quality posts | |||
| Apr 26, 2017 at 23:33 | |||||
| Apr 26, 2017 at 22:59 | history | edited | YCor |
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| Apr 26, 2017 at 22:42 | comment | added | Gerhard Paseman | See mathoverflow.net/questions/61744 to get an idea of a solution. This is the wrong forum for your question. Gerhard "Trying Small Examples Helps Much" Paseman, 2017.04.26. | |
| Apr 26, 2017 at 22:41 | review | First posts | |||
| Apr 26, 2017 at 22:55 | |||||
| Apr 26, 2017 at 22:37 | history | asked | Willliam D. Weakley | CC BY-SA 3.0 |