Timeline for Polynomial whose values divide $n!$
Current License: CC BY-SA 4.0
15 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jul 25, 2022 at 22:52 | vote | accept | Yessir03 | ||
| Sep 1, 2021 at 20:24 | vote | accept | Yessir03 | ||
| Sep 1, 2021 at 20:25 | |||||
| Sep 1, 2021 at 20:24 | vote | accept | Yessir03 | ||
| Sep 1, 2021 at 20:24 | |||||
| Jul 13, 2021 at 13:18 | comment | added | Yaakov Baruch | @Pasten: I managed to generalize your example into a complete answer (barring typos). | |
| Jul 13, 2021 at 13:15 | answer | added | Yaakov Baruch | timeline score: 8 | |
| Jul 12, 2021 at 13:21 | comment | added | Pasten | @YaakovBaruch Yes. You can prove this with the large sieve for instance. In general, for the hard questions about primes, the upper bound for counting can be shown using a sieve, while the lower bound is not known. | |
| Jul 12, 2021 at 10:19 | comment | added | Yaakov Baruch | @Pasten: Is it known that the values of a quadratic polynomial cannot be prime with positive density? | |
| Jul 12, 2021 at 0:15 | comment | added | Pasten | Here is an example that might help: p(x)=x^2+4. Put x=t^2 and note that p(t^2)=f(t)g(t) with f,g quadratic. Unconditionally, one can show by a simple sieve that f(t), g(t) have a positive density of simultaneous coprime squarefree values (except, perhaps, for a fixed small factor I didn't check.) Discarding prime values of f and g, you are done with this example. | |
| S Jul 12, 2021 at 0:05 | history | suggested | markvs | CC BY-SA 4.0 |
corrected misprints, added examples
|
| Jul 11, 2021 at 22:56 | review | Suggested edits | |||
| S Jul 12, 2021 at 0:05 | |||||
| Jul 11, 2021 at 22:24 | history | edited | Wojowu | CC BY-SA 4.0 |
added 48 characters in body; edited title
|
| Jul 11, 2021 at 22:17 | answer | added | Stanley Yao Xiao | timeline score: 6 | |
| Jul 11, 2021 at 22:06 | history | edited | Yessir03 | CC BY-SA 4.0 |
added 70 characters in body
|
| Jul 11, 2021 at 18:18 | comment | added | YCor | I assume the question is "Does there always exist..."? Where does the question arise from? | |
| Jul 11, 2021 at 17:46 | history | asked | Yessir03 | CC BY-SA 4.0 |