Timeline for Divisibility relation with a specific sum of divisors
Current License: CC BY-SA 4.0
12 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Nov 28, 2022 at 11:06 | vote | accept | JoshuaZ | ||
| Nov 28, 2022 at 6:59 | answer | added | Alapan Das | timeline score: 3 | |
| Nov 27, 2022 at 19:33 | comment | added | Max Alekseyev | @JoshuaZ: Multiply the first (Touchard's) identity in that question by $\sigma(n)$ and subtract the third (Ramanujan's) one multiplied by $18n^2$... | |
| Nov 27, 2022 at 16:01 | comment | added | JoshuaZ | @darijgrinberg Hmm, they say that it follows directly from the Touchard and Ramanujan identities there, but I'm not seeing it. | |
| Nov 27, 2022 at 15:33 | comment | added | darij grinberg | To be honest, I'm not fully sure if (and where) that formula for $A_2\left(n\right)$ is proved... | |
| Nov 27, 2022 at 11:44 | comment | added | JoshuaZ | @darijgrinberg Yes, that works! If you put it in an answer I'll accept it. | |
| Nov 27, 2022 at 3:47 | comment | added | darij grinberg | (To spell it out: The claim follows easily from the formula for $A_2\left(n\right)$ in mathoverflow.net/a/372770 , combined with a short modulo-$3$ argument using Fermat's Little Theorem $a^3 \equiv a \mod 3$.) | |
| Nov 27, 2022 at 3:43 | comment | added | darij grinberg | Huh, MO suggests mathoverflow.net/questions/372766/… as a related link. Good job, MO! | |
| Nov 27, 2022 at 3:40 | comment | added | Max Alekseyev | For symmetry $k^2$ can be replaced with $k(n-k)$. | |
| Nov 27, 2022 at 3:37 | comment | added | darij grinberg | Note that you can replace the upper limit of the sum by $n-1$. This results in a more natural question (which, however, is equivalent to yours, since $k^2 \equiv \left(n-k\right)^2 \mod n$). | |
| Nov 27, 2022 at 3:24 | history | edited | LSpice | CC BY-SA 4.0 |
`|` -> `\mid`, repeated word, and name of MO question
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| Nov 27, 2022 at 3:07 | history | asked | JoshuaZ | CC BY-SA 4.0 |