Timeline for Non-trivial solution to $\sum^{n}_{i=1}\sum^{n}_{j=1,j\ne i}(x_{i})^{(x_j)}=(\sum^{n}_{i=1}x_i)^{(\sum^{n}_{i=1}x_i)}$
Current License: CC BY-SA 4.0
32 events
| when toggle format | what | by | license | comment | |
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| S Jul 3, 2021 at 6:00 | history | bounty ended | CommunityBot | ||
| S Jul 3, 2021 at 6:00 | history | notice removed | CommunityBot | ||
| Jul 2, 2021 at 23:42 | history | edited | Alex-Github-Programmer | CC BY-SA 4.0 |
Corrected LaTeX
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| Jul 2, 2021 at 23:35 | history | edited | Alex-Github-Programmer | CC BY-SA 4.0 |
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| Jul 2, 2021 at 17:35 | comment | added | mathlove | $2+\frac{(n-2)(n-1)}2$ is equal to $\frac{n^2-3n+6}{2}$, not $\frac{n^2-3n-6}{2}$. | |
| Jul 2, 2021 at 11:58 | comment | added | mathlove | A nice work, but I think you have a typo. What you got is $S^{S_n}\le\dfrac{n^2-3n\color{red}+6}2$ from which I got $x_1=x_2=\cdots =x_{\lfloor 2n/3\rfloor}=0$ which is slightly better than claim 3 in my answer. | |
| Jul 2, 2021 at 7:12 | answer | added | mathlove | timeline score: 1 | |
| Jul 2, 2021 at 6:19 | answer | added | Alex-Github-Programmer | timeline score: 0 | |
| Jul 2, 2021 at 6:06 | history | edited | Alex-Github-Programmer | CC BY-SA 4.0 |
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| Jul 2, 2021 at 1:54 | comment | added | Alex-Github-Programmer | @mathlove Could you post your comment as an answer? Also show your process. | |
| Jun 26, 2021 at 16:38 | answer | added | Peter Taylor | timeline score: 4 | |
| Jun 26, 2021 at 14:19 | history | rollback | Alex-Github-Programmer |
Rollback to Revision 5
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| Jun 26, 2021 at 14:19 | history | rollback | Alex-Github-Programmer |
Rollback to Revision 6
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| Jun 26, 2021 at 14:11 | comment | added | Alex-Github-Programmer | @PeterTaylor I see. | |
| Jun 26, 2021 at 12:42 | comment | added | mathlove | If I'm not mistaken, $x_1=x_2=\cdots =x_{\lfloor (2n-1)/3\rfloor}=0$. | |
| Jun 26, 2021 at 11:13 | history | edited | Alex-Github-Programmer | CC BY-SA 4.0 |
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| Jun 26, 2021 at 10:42 | comment | added | Peter Taylor | (Also, by exhaustive checking, $S=2$ giving the known non-trivial example or $S > 95$). | |
| Jun 26, 2021 at 10:12 | comment | added | mathlove | A slightly better claim can be obtained. One can prove that for every non-trivial solution to $A_n$, $S^{S_n}\le n(n-1)/2$. I've already got the following small results, but don't know how to do for larger $n$. (1) $x_1=0$. (2) If $n\ge 4$, then $x_2=0$. (3) If $n\ge 6$, then $x_3=0$. (4) $A_2$ has no non-trivial solution. (5) $A_3$ has only one non-trivial solution. (6) Each of $A_4,A_5,A_6,A_7$ has no non-trivial solution. | |
| Jun 26, 2021 at 9:39 | history | edited | Alex-Github-Programmer | CC BY-SA 4.0 |
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| Jun 26, 2021 at 8:45 | history | edited | Alex-Github-Programmer | CC BY-SA 4.0 |
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| Jun 25, 2021 at 4:07 | history | edited | Alex-Github-Programmer | CC BY-SA 4.0 |
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| S Jun 25, 2021 at 4:01 | history | bounty started | Alex-Github-Programmer | ||
| S Jun 25, 2021 at 4:01 | history | notice added | Alex-Github-Programmer | Draw attention | |
| Jun 20, 2021 at 11:57 | comment | added | Max Lonysa Muller | @Alex-Github-Programmer interesting family of equations. Do you have an application in mind for this problem? | |
| Jun 20, 2021 at 9:34 | history | edited | YCor | CC BY-SA 4.0 |
fixed title and formatted link
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| Jun 19, 2021 at 23:39 | comment | added | Alex-Github-Programmer | @BrendanMcKay And for odd square $t$ it is also close to the square $(2t^{t/2})^2$. | |
| Jun 19, 2021 at 23:28 | history | edited | Alex-Github-Programmer | CC BY-SA 4.0 |
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| Jun 19, 2021 at 14:19 | comment | added | Brendan McKay | $4t^t+(t-1)(3t+1)$ is a square for $t=2$. If it is ever a square for larger integer $t$, that will give another 0-1 solution. It doesn't happen up to $t=10000$. For even $t$, it is too close to the square $(2t^{t/2})^2$; I'm not sure about odd $t$. | |
| Jun 19, 2021 at 13:49 | comment | added | Gerald Edgar | I agree with @BrendanMcKay ... as given I would inerpret this in real numbers. Well, positive real numbers so that the powers are also real. In integers, you could allow negative values. | |
| Jun 19, 2021 at 13:28 | comment | added | Brendan McKay | You want integers or real numbers? | |
| Jun 19, 2021 at 7:25 | review | First posts | |||
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| Jun 19, 2021 at 7:19 | history | asked | Alex-Github-Programmer | CC BY-SA 4.0 |