Let $\alpha$ be algebraic over $F$. Suppose the degree of $\alpha$ over $F$ is odd. Show that $F(\alpha)=F(\alpha^2)$?
7567
Degree of Field Extensions and $F(\alpha)$
41505
Transcendental Extensions. $F(\alpha)$ isomorphic to $F(x)$
40502
The Degree of Zero Polynomial.
81775
Prove $a^\alpha b^{1-\alpha} \le \alpha a + (1 - \alpha)b, \; a,b > 0,\; 0 < \alpha < 1$
52212
If $\alpha$ is an algebraic element and $L$ a field, does the polynomial ring $L[\alpha]$ is also a field?
85459
$x^3+x+1$ irreducible over $\mathbb{F}_2$, $\theta$ root, compute powers of $\theta$
43300
The degree of $\sqrt{2} + \sqrt[3]{5}$ over $\mathbb Q$
21972
How to show that $\sqrt{2}+\sqrt{3}$ is algebraic?
92537
Prove that $f(x)\in \mathbb{Z}[x]$ such that $f(0)$ and $f(1)$ are odd has no integer roots
6722
to show $f$ is a polynomial in $z$
98968
$X$ is algebraic over $E$
145507
Is $K[a,b]=K(a,b)$ for algebraic $a, b$?
13147
Proof verification - Minimal polynomial of $\alpha$ has integer coef.s iff its an alg. integer
148310
Showing rational numbers are algebraic
48268
How many $\alpha \in S_n$ are such that $\alpha^2 = 1$?
148486
Suppose $f$ is entire and $|f(z)| \leq A + B |z|^{3/2}$. Show that $f$ is a linear polynomial.
28803
Extension of degree 2 with characteristic not 2