Timeline for Polynomial whose values divide $n!$
Current License: CC BY-SA 4.0
10 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Sep 1, 2021 at 20:24 | vote | accept | Yessir03 | ||
| Sep 1, 2021 at 20:25 | |||||
| Jul 12, 2021 at 7:36 | comment | added | Fedor Petrov | we do not actually need $f(n)$ be square free: if $p$ divides $f(n)$ and $p<\sqrt{n}$, then we have something like $\nu_p(n)<3\log_2n<\nu_p(n!)$ | |
| Jul 12, 2021 at 2:46 | comment | added | markvs | The fact that $f(g(t))=f_1(t)⋯f_m(t)$ with the $f_j$'s pairwise co-prime is true for every $f,g$ and follows from PID. | |
| Jul 12, 2021 at 1:18 | comment | added | markvs | The argument is less clear now. What is "large" $X$? What is $\epsilon$ and what is $\gg_\epsilon$? The number $k$ is first defined as the product of some primes $<X$ and then is bound by $\exists$. Why is $g(n)/p> g(n)^{1-\epsilon}$ (what if $p=g(n)$?)? | |
| Jul 12, 2021 at 0:37 | comment | added | Stanley Yao Xiao | @MarkSapir the argument ended up being more intricate than I thought, and requires looking at the actual proofs in the paper rather than just the statement of the main theorems. Luckily what they proved is enough to imply the result, without any new insights | |
| Jul 12, 2021 at 0:36 | history | edited | Stanley Yao Xiao | CC BY-SA 4.0 |
added 2366 characters in body
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| Jul 11, 2021 at 23:22 | comment | added | markvs | I do not think the result in the paper implies the result you want to prove, at least easily. | |
| Jul 11, 2021 at 23:04 | comment | added | Stanley Yao Xiao | @MarkSapir ah yes I agree... but nevertheless the given paper still implies the desired result. I will edit my answer | |
| Jul 11, 2021 at 22:58 | comment | added | markvs | "If $n$ is such that whenever $p|f(n)$ we have $p\le n$ then the desired outcome is true." That claim and the rest of the answer are incorrect. | |
| Jul 11, 2021 at 22:17 | history | answered | Stanley Yao Xiao | CC BY-SA 4.0 |