$\alpha$ root of $x^{p^{d}} - x$ then it is a root of $x^{p^{ds}} - x$
39217
If $d \mid n$ then $x^{q^d} - x \mid x^{q^n} - x$.
81778
If $m|n$ and $a$ is a primitive root of $n$, show that $a$ is a primitive root of $m$ (understanding a tip)
4706
Prove $f=x^p-a$ either irreducible or has a root. (arbitrary characteristic) (without using the field norm)
121100
Rootspaces are $\mathop{ad}$ nilpotent
46106
Prove that $D_r \circ D_s = \{ (x,y) \in \mathbb{R}^2 \ | \ |x-y|<r+s \}$, where $D_a = \{ (x,y) \in \mathbb{R}^2\ | \ |x-y| < a \}$
121076
Show $x^p-t$ has no root in the field $\mathbb{F}_p(t)$
153862
A question about a primitive root mod $p=2^{2^k}+1$, where $p$ is prime.
146312
Is the set of roots with respect to their values and multiplicies unique for each $g(x)$ in $a_n x^n + g(x)$?
55197
Roots of $ x^3-3x+1$
2614
Prove that , any primitive root $r$ of $p^n$ is also a primitive root of $p$
75639
Showing that $\sqrt[3]{2}\notin\Bbb Q(\alpha_1,...,\alpha_k)$ where $\alpha_i^2\in\Bbb Q\ \forall i$
61148
Finding real roots of $ P(x)=x^8 - x^7 +x^2 -x +15$
90273
Primitive roots of the unity in $\mathbb C$
127622
Does there exist a $1$-form $\alpha$ with $d\alpha = \omega$?
59416
Quadratic residues and index w.r.t. primitive root of a odd prime p
145509
Prove the roots of $p(z)+z^n\bar{p}(\frac{1}{z})$ lie on the unit circle
95594
Prove that a polynomial is irreducible or the field contains a $p$th root