Timeline for find a set of integers where {$a_i + a_j | 1 \le i \le j \le n$} leave distinct remainders when divided by $n(n+1)/2$
Current License: CC BY-SA 4.0
7 events
| when toggle format | what | by | license | comment | |
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| Jun 21, 2018 at 17:44 | comment | added | Gerhard Paseman | I agree that it is a proof sketch, not a fallacy, and that you don't need to explain further to me. If you wanted to rewrite it to avoid traps like the one I fell in, reinforcing the idea that the assumption implies all 2(N-n) nonzero differences must be distinct is important. Not everyone will think you were trying to give a bijection from the set of differences to the set of sums. Once again, a brilliant example, and thank you. Gerhard "This Deserves My Next Upvote" Paseman, 2018.06.21. | |
| Jun 21, 2018 at 17:37 | comment | added | Seva | @GerhardPaseman: the bottom line is, you agree - or should I further explain anything? | |
| Jun 21, 2018 at 17:19 | comment | added | Gerhard Paseman | Bijecting, not bisecting. Gerhard "Ran Out Of Edit Time" Paseman, 2018.06.21. | |
| Jun 21, 2018 at 17:12 | comment | added | Gerhard Paseman | Ah. For me, the missing step is "if ai - aj agrees with as-at mod N, then (since at is not as) either i=s and j=t or else two sums are also the same mod N, so the assumption implies there have to be n(n-1) distinct nonzero differences mod N." I vote proof now. (Originally, I thought you were bisecting differences to sums.) Gerhard "Thank You For Your Patience" Paseman, 2018.06.21. | |
| Jun 21, 2018 at 16:56 | comment | added | Gerhard Paseman | To be clear, I think this is a brilliant example, and I want it to stay. I am just not clear if it is an example of proof or of fallacy. Gerhard "We Need To Understand These" Paseman, 2018.06.21. | |
| Jun 21, 2018 at 16:49 | comment | added | Gerhard Paseman | This is a really clever sleight of mind argument. Can you expand on the word "Thus", as I am not seeing how what follows "Thus" is a consequence of what comes before? Gerhard "Otherwise It Is Quite Nice" Paseman, 2018.06.21. | |
| Jun 20, 2018 at 5:51 | history | answered | Seva | CC BY-SA 4.0 |