Timeline for A new simple formula is needed
Current License: CC BY-SA 4.0
9 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Feb 22, 2021 at 19:03 | vote | accept | Maksym Voznyy | ||
| Feb 4, 2021 at 5:10 | vote | accept | Maksym Voznyy | ||
| Feb 22, 2021 at 19:02 | |||||
| Jan 25, 2021 at 3:33 | comment | added | Maksym Voznyy | The formulas with $s=4$ that could have been included in my original question: (15) $b=\dfrac{4a(a+1)}{21a^2+6a+1}$, (16) $b=\dfrac{(a-1)^2}{15a^2+18a-1}$, (17) $b=\dfrac{a(a+1)}{24a^2+9a+1}$. And a new one with $s=2$: (18) $b=-(2a+1)^2$, this seed will produce many more! This discussion opened a new universe for me, thank you so much, everybody! Promise to update here if/when the new high rank $\mathbb{Z}/6\mathbb{Z}$ curves are produced by any of these formulas. Back to searching for rank 8, rank 9 and above! | |
| Jan 25, 2021 at 3:09 | vote | accept | Maksym Voznyy | ||
| Feb 4, 2021 at 5:10 | |||||
| Jan 24, 2021 at 18:42 | comment | added | Maksym Voznyy | Six more formulas with $s=4$ derived from (6) due to Nulhomologous, all true for any $r$: (9) $b=\dfrac{(4a+3)^2}{240a^2+232a-9}$, (10) $b=\dfrac{(23a-1)^2}{495a^2+1070a-1}$, (11) $b=\dfrac{(5a+6)^2}{231a^2+196a-36}$, (12) $b=\dfrac{256a(a+1)}{273a^2-302a+1}$, (13) $b=\dfrac{(a+3)^2}{255a^2+250a-9}$, (14) $b=\dfrac{64a(a+1)}{465a^2-110a+1}$. | |
| Jan 24, 2021 at 16:41 | comment | added | Maksym Voznyy | Applying the new formula (6) and (1) consecutively: (7) $b=\dfrac{(4a+3)^2}{48a^2+40a-9}$, $s=4$. Applying (1) and (6) consecutively: (8) $b=\dfrac{64a(a+1)}{(3a-1)(35a-1)}$, $s=4$. | |
| Jan 24, 2021 at 16:04 | comment | added | Maksym Voznyy | Thank you so much! This is exactly an example of a new formula I was looking for! The formula is true for any $a$ and any $r$, and is simple ($s=3$). Could there be more of them with $s\le6$? Did you use brute-force or any other approach? In what math package? | |
| Jan 24, 2021 at 11:11 | review | Low quality posts | |||
| Jan 24, 2021 at 11:16 | |||||
| Jan 24, 2021 at 10:54 | history | answered | Nulhomologous | CC BY-SA 4.0 |