query: Prove or disprove that $[L:K] = \deg(p)$
positive_passages.docid: 26999
positive_passages.text: How is the degree of the minimal polynomial related to the degree of a field extension?
negative_passages.docid: 51465
negative_passages.text: New, elegant proofs for $\varphi(p^{k})=p^{k}-p^{k-1}$
negative_passages.docid: 62224
negative_passages.text: Need help with proof for Dedekind cuts on $\mathbb{Q}^+$
negative_passages.docid: 155190
negative_passages.text: Stone-Weierstrass theorem with $p(1/x)$
negative_passages.docid: 106401
negative_passages.text: Prove: $p-mq | f(m)$ where $m$ is any integer
negative_passages.docid: 30630
negative_passages.text: Proving ${n \choose p} \equiv \Bigl[\frac{n}{p}\Bigr] \ (\text{mod} \ p)$
negative_passages.docid: 94469
negative_passages.text: How to prove that $|HK| = \dfrac{|H| \; |K|}{|H \cap K|}$?
negative_passages.docid: 60761
negative_passages.text: Proof: $\cos^p (\theta) \le \cos(p\theta)$
negative_passages.docid: 65764
negative_passages.text: Partitioning $\{1,2,\ldots,k\}$ into $p$ subsets with equal sums, where $p$ is prime
negative_passages.docid: 68153
negative_passages.text: How to show that $L^p$ spaces are nested?
negative_passages.docid: 136844
negative_passages.text: Mathematical induction question: why can we "assume $P(k)$ holds"?
negative_passages.docid: 139674
negative_passages.text: Prove $\ln\frac{p}{q}\leq \frac{p-q}{\sqrt{pq}}$ for $0<q\leq p$
negative_passages.docid: 21250
negative_passages.text: Prove $x \equiv a \pmod{p}$ and $x \equiv a \pmod{q}$ then $x \equiv a\pmod{pq}$
negative_passages.docid: 145752
negative_passages.text: Aut $\mathbb Z_p\simeq \mathbb Z_{p-1}$
negative_passages.docid: 3273
negative_passages.text: Trouble in proving that $\|x\|_p = \max|x_j|$
negative_passages.docid: 102079
negative_passages.text: If $1\leq p < \infty$ then show that $L^p([0,1])$ and $\ell_p$ are not topologically isomorphic
negative_passages.docid: 5841
negative_passages.text: Proving prime $p$ divides $\binom{p}{k}$ for $k\in\{1,\ldots,p-1\}$