Timeline for An identity related to sum of two squares
Current License: CC BY-SA 4.0
15 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| yesterday | vote | accept | Tong Lingling | ||
| yesterday | history | edited | Tong Lingling | CC BY-SA 4.0 |
improve formatting
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| yesterday | comment | added | Tong Lingling | @Luna'sChalkboard I have verified the case for $k\leqslant 10^5$ and found no counterexamples. I will update in this post after extending the verification to a larger range. | |
| yesterday | history | became hot network question | |||
| yesterday | comment | added | David E Speyer | I answered a similar question at mathoverflow.net/questions/442497 . | |
| yesterday | answer | added | Henri Cohen | timeline score: 8 | |
| 2 days ago | comment | added | Tong Lingling | @DanielWeber Sorry for my typo. '$r$ divides $m$' should be replaced with '$r$ divides $j$'. | |
| 2 days ago | history | edited | Tong Lingling | CC BY-SA 4.0 |
correct typo
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| 2 days ago | comment | added | Tong Lingling | @DanielWeber I've edited and supplemented some steps. It makes use of the identity $\left\lfloor\frac{j^2}{m}\right\rfloor + \left\lfloor\frac{j'^2}{m}\right\rfloor = \frac{j^2}{m}+\frac{j'^2}{m}+\epsilon$, where $\epsilon=0$ if $r$ divide $m$, and $\epsilon=-1$ in other case. | |
| 2 days ago | history | edited | Tong Lingling | CC BY-SA 4.0 |
supplement content
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| 2 days ago | comment | added | EffingLoveMath | Why is your set of test cases so small? Usually, we test all $k = 1...N$ and numbers $m=4k+1$ that meet the conditions, where $N = 20...10,000$ the higher the more confident we can be to proceed with the proof assuming no counter-example was found. | |
| 2 days ago | comment | added | Daniel Weber | Could you explain how to get from $\frac{1}{2}\sum_{j=1}^{2k}\left(\left\lfloor\frac{j^2}{m}\right\rfloor+\left\lfloor\frac{j'^2}{m}\right\rfloor\right)$ to $\frac{2k(k-1)}{3}+\frac{1}{2}\left\lfloor\frac{2k}{r}\right\rfloor $? | |
| 2 days ago | history | edited | Tong Lingling | CC BY-SA 4.0 |
correct
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| 2 days ago | history | edited | Tong Lingling | CC BY-SA 4.0 |
delete tag 'prime'
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| 2 days ago | history | asked | Tong Lingling | CC BY-SA 4.0 |