Timeline for $x^2+7y^2=2^n$ and sums of four squares
Current License: CC BY-SA 4.0
17 events
| when toggle format | what | by | license | comment | |
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| Oct 16, 2020 at 19:34 | comment | added | Anthony Quas | For what it’s worth, I value conjectures like this on MO. more generally I see posing conjectures as an under-valued activity, even if some of the conjectures turn out to be easily settled. | |
| Oct 16, 2020 at 15:09 | comment | added | Zhi-Wei Sun | If you consider my questions or conjectures posted on MathOverflow not reasonable or not deep, you may either prove it completely or disprove it. | |
| Oct 16, 2020 at 14:50 | comment | added | Zhi-Wei Sun | I don't think one can only ask reference-request type questions on MathOverFlow. People here are clever mathematicians and they need new challenging problems. | |
| Oct 16, 2020 at 14:45 | comment | added | Zhi-Wei Sun | @Will Jagy I have stopped to send messages to Number Theory List for at least three years. | |
| Oct 16, 2020 at 14:43 | comment | added | Zhi-Wei Sun | Yes, I do have many mathematical questions or conjectures. If people here do not like me to raise my own questions, I'll consider to quit from MathOverFlow and delete all my postings. | |
| Oct 16, 2020 at 14:37 | comment | added | Will Jagy | @WhatsUp yes, and on NMBRTHRY for years and years and years listserv.nodak.edu/cgi-bin/wa.exe?A0=NMBRTHRY archives | |
| Oct 16, 2020 at 0:39 | comment | added | Zhi-Wei Sun | @AlexB. Yes, I agree as I mentioned before. | |
| Oct 16, 2020 at 0:38 | comment | added | Zhi-Wei Sun | For any question, one might have his/her own opinion whether the answer is positive or not. If quite sure, then that's a conjecture. | |
| Oct 15, 2020 at 23:27 | comment | added | WhatsUp | @Alex My feeling is that the OP uses this site as a place to advertise his "conjectures", many of which are just experimental results without much thought. See all his other posts. | |
| Oct 15, 2020 at 23:07 | history | edited | KConrad | CC BY-SA 4.0 |
filled in details near the end
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| Oct 15, 2020 at 11:05 | comment | added | Alex B. | @Zhi-WeiSun: this looks to me like a pretty exhaustive answer to your actual question "What nontrivial things can we say about the diophantine equation $x^2+7y^2=2^n$. | |
| Oct 15, 2020 at 4:48 | comment | added | Zhi-Wei Sun | Note that even requiring $x+24y$ is a square when we write $n=x^2+y^2+z^2+w^2$ is difficult to prove. My challenging 24-conjecture states that any $m\in\mathbb N$ can be written as $x^2+y^2+z^2+w^2$ $ (x,y,z,w\in\mathbb N)$ with $x$ and $x+24y$ both squares. | |
| Oct 15, 2020 at 4:44 | comment | added | Zhi-Wei Sun | Your solution to the equation $x^2+7y^2=2^n$ is fine, it should be treated as a partial answer. | |
| Oct 15, 2020 at 4:18 | comment | added | KConrad | So do you want me to delete my answer because of that? I am just showing that solutions in odd numbers to $x^2 + 7y^2 = 2^n$ (for $n \geq 3$) can be very easily described. Solutions in even numbers (for varying $n$) must come from multiplying an odd solution by powers of 2, so there is nothing deep about the integral solutions to this Diophantine equation. | |
| Oct 15, 2020 at 4:16 | comment | added | Zhi-Wei Sun | Thanks. But this does not imply the conjecture. | |
| Oct 15, 2020 at 4:11 | history | edited | KConrad | CC BY-SA 4.0 |
deleted 30 characters in body
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| Oct 15, 2020 at 4:06 | history | answered | KConrad | CC BY-SA 4.0 |