query: Prove that $F[x]/(f(x))$ has $q^n$ elements
positive_passages.docid: 51770
positive_passages.text: Number of elements in a finite field extension for finite fields
negative_passages.docid: 146665
negative_passages.text: Prove that $f(x)=8$ for all natural numbers $x\ge{8}$
negative_passages.docid: 86877
negative_passages.text: Let $F$ be a Galois extension over $\mathbb{Q}$ with $[F:\mathbb{Q}]=2^n$, then all elements in $F$ are constructible
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: 60348
negative_passages.text: How do I prove $F(a)=F(a^2)?$
negative_passages.docid: 6722
negative_passages.text: to show $f$ is a polynomial in $z$
negative_passages.docid: 91914
negative_passages.text: Prove that for the Fibonacci sequence $(F_n)$, $F_n$ divides $F_{2n}$.
negative_passages.docid: 81223
negative_passages.text: Real Analysis Question: continuity of $f(x) = \sum_{q_n<x} 1/n^2$
negative_passages.docid: 106284
negative_passages.text: Establishing a Basis for $F[x]/(f(x))$
negative_passages.docid: 141852
negative_passages.text: Prove that $2\int_a^b \int_a^x f(x)f(y) \, dy \, dx = \left[ \int_a^b f(x) \, dx \right]^2$
negative_passages.docid: 13253
negative_passages.text: Prove $f(S \cup T) = f(S) \cup f(T)$
negative_passages.docid: 118299
negative_passages.text: Show that $(\mathbb{Z}[x]/(x^{n+1}))^{\times}\cong \mathbb{Z}/2\mathbb{Z}\times\Pi_{i=1}^n\mathbb{Z}$
negative_passages.docid: 49953
negative_passages.text: Proving that a function from $N\times N$ to $N$ is bijective.
negative_passages.docid: 14830
negative_passages.text: A transformation of F[x]
negative_passages.docid: 153406
negative_passages.text: $[F(t):F(t^n)]=n$ where $t$ is trascendental
negative_passages.docid: 20467
negative_passages.text: Show that $(y_n)\in l^q$
negative_passages.docid: 78143
negative_passages.text: Proving $\mathbb{F}_p/\langle f(x)\rangle$ with $f(x)$ irreducible of degree $n$ is a field with $p^n$ elements