Timeline for Divisibility chains and polynomials
Current License: CC BY-SA 4.0
9 events
| when toggle format | what | by | license | comment | |
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| Sep 21, 2022 at 2:21 | history | became hot network question | |||
| Sep 20, 2022 at 20:41 | comment | added | Zach Hunter | I agree there is a probably an interesting question there. however such a result would be incomparable with the factorial problem, since the conjecture is that $R_P$ only contains finitely many factorials (which could be absurdly spaced apart). | |
| Sep 20, 2022 at 19:24 | comment | added | Ofir Gorodetsky | Although my answer shows that any $P$ is a counter-example, maybe there is a modification for which there are no counter-examples, which is in between your notion (no infinite divisibility chain) and the factorial problem. For instance, requiring the infinite divisibility chain to satisfy a growth condition such as $a_{i+1}/a_i$ being at most $O(i^C)$ or even $e^{O(i)}$. My current counter-examples involve $a_{i+1}/a_i$ being huge (super exponential). | |
| Sep 20, 2022 at 18:53 | vote | accept | Zach Hunter | ||
| Sep 20, 2022 at 18:49 | answer | added | Ofir Gorodetsky | timeline score: 8 | |
| Sep 20, 2022 at 18:46 | history | edited | Zach Hunter | CC BY-SA 4.0 |
added 186 characters in body
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| Sep 20, 2022 at 18:37 | comment | added | Zach Hunter | @OfirGorodetsky ah, this thwarts my question. perhaps that is a reason why the case of $x^2-1$ is open for the factorial question. I guess I will amend the question. | |
| Sep 20, 2022 at 18:28 | comment | added | Ofir Gorodetsky | You surely want to add some condition. E.g. if $P(x)=x^2-1$ you get an infinite divisibility chain by considering $P(2^{2^n})$. | |
| Sep 20, 2022 at 18:18 | history | asked | Zach Hunter | CC BY-SA 4.0 |