Timeline for Polynomials which always assume perfect power values
Current License: CC BY-SA 3.0
5 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Apr 16, 2017 at 23:07 | vote | accept | Stanley Yao Xiao | ||
| Nov 30, 2015 at 10:35 | comment | added | Peter Mueller | @WillSawin: This proof is much more elementary after noting that it is not necessary to use Cebotarev (or Frobenius) here: Let $F(x)\in\mathbb Z[x]$ be the minimal polynomial of an integral primitive element of the splitting field of $f(x)$. Then for any prime $p$ dividing $F(m)$ for some integer $m$ for which $F(x)$ is separable modulo $p$ we get that $F(x)$ factors into linears modulo $p$, and so does $f(x)$. Running through $m\in\mathbb Z$, we get infinitely primes of the required form. | |
| Nov 30, 2015 at 8:58 | comment | added | Will Sawin | It's not clear to me if this argument is more elementary because it uses $L$ functions, but I'm glad you solved the more general version. | |
| Nov 30, 2015 at 8:05 | review | First posts | |||
| Nov 30, 2015 at 8:08 | |||||
| Nov 30, 2015 at 8:02 | history | answered | user83446 | CC BY-SA 3.0 |