query: Show that $F(a) = F(a^{2})$ knowing that $F(a)$ has odd degree.
positive_passages.docid: 24466
positive_passages.text: Prove that if $[F(\alpha):F]$ is odd then $F(\alpha)=F(\alpha^2)$
negative_passages.docid: 61799
negative_passages.text: Prove that $\Vert f(b)-f(a)-f'(a)(b-a) \Vert\leq \sup_{x\in [a,b]} \Vert f''(x)\Vert\Vert b-a\Vert^2$
negative_passages.docid: 24553
negative_passages.text: $f$ has the form $f(x) =ax^2+bx+c$.
negative_passages.docid: 149634
negative_passages.text: $ 2|f^{'}(0)| = \sup_{z, w \in D} |f(z)-f(w)|$
negative_passages.docid: 154288
negative_passages.text: proof that Even powers of an odd function's taylor polynomial vanish
negative_passages.docid: 83291
negative_passages.text: Prove that $p(x)=(x-a)q(x)$ for some $q(x)\in R[x]$ of degree= (degree of $p)-1$.
negative_passages.docid: 24810
negative_passages.text: Functions satisfying $(b-a)f'(\tfrac{a+b}{2}) = f(b)- f(a)$
negative_passages.docid: 131692
negative_passages.text: How to show that $f_{0}f_{1}+f_{1}f_{2}+...+f_{2n-1}f_{2n} = f^{2}_{2n}$
negative_passages.docid: 45037
negative_passages.text: Show $(2^m-1,2^n+1)=1$ if $m$ is odd
negative_passages.docid: 155444
negative_passages.text: Show that entire function $f$ is a polynomial of degree at most $n$
negative_passages.docid: 8494
negative_passages.text: Proof Check: Number of elements of $\mathbb{F}_{p^{n}}$ of the form $a^{p}-a$ for some $a \in \mathbb{F}_{p^{n}}$.
negative_passages.docid: 13270
negative_passages.text: Prove $\exists \xi \in (a,b):f'(\xi)<1+f^2(\xi)$
negative_passages.docid: 82567
negative_passages.text: Prove that $ f(x) $ has at least two real roots in $ (0,\pi) $
negative_passages.docid: 66703
negative_passages.text: Show that $8 \mid (a^2-b^2)$ for $a$ and $b$ both odd
negative_passages.docid: 153532
negative_passages.text: Proving $a^2$ is even $\implies$ $a$ is even by contradiction
negative_passages.docid: 158862
negative_passages.text: Show that $a(-1) = (-1)a = -a $.
negative_passages.docid: 155828
negative_passages.text: How do I show that $A$ and $A^T$ are similar, given that the minimal polynomial of $A$ splits over $\mathbb{F}$?