query: Prove that $D_n$ is generated by ⟨r,f⟩
positive_passages.docid: 25624
positive_passages.text: Show the Dihedral Group $D_n$ is generated by rotations and reflection along the x axis.
negative_passages.docid: 11289
negative_passages.text: Why $d(x) + d(y) \le n$ when proving Mantel's theorem
negative_passages.docid: 70128
negative_passages.text: Prove that $(fg)^{(n)} = \sum_{k=0}^n \binom{n}{k}f^{(k)}(x)g^{(n-k)}(x)$
negative_passages.docid: 91980
negative_passages.text: Prove that f is one-to-one on D
negative_passages.docid: 100515
negative_passages.text: Prove that if $d$ divides $n$ then $φ(d)$ divide $φ(n)$ for $φ$ denotes Euler’s φ-function.
negative_passages.docid: 14759
negative_passages.text: Prove that $ f(z) = 0 $ for all $ z \in \overline{D}(0,1) $.
negative_passages.docid: 24912
negative_passages.text: Show that if $fd'=f'd $ and the pairs $f, d $ and $f',d' $ are coprime, then $f=f' $ and $d=d' $.
negative_passages.docid: 57193
negative_passages.text: Prove that $f$ has derivatives of all orders at $x=0$, and that $f^{(n)}(0)=0$ for $n=1,2,3\ldots$
negative_passages.docid: 106698
negative_passages.text: $\mathbb N$ when given the metric $d(m,n)=\frac{1}{m}-\frac{1}{n}$
negative_passages.docid: 30630
negative_passages.text: Proving ${n \choose p} \equiv \Bigl[\frac{n}{p}\Bigr] \ (\text{mod} \ p)$
negative_passages.docid: 147661
negative_passages.text: Show that {$x_n$} is a convergent sequence if $d(x_{n+2}, x_{n+1})≤ rd(x_{n+1}, x_n)$
negative_passages.docid: 152932
negative_passages.text: Proof: $\det\pmatrix{\langle v_i , v_j \rangle}\neq0$ $\iff \{v_1,\dots,v_n\}~\text{l.i.}$
negative_passages.docid: 46563
negative_passages.text: Show that the quotient space is homeomorphic to the n-disc
negative_passages.docid: 91081
negative_passages.text: Prove that, for every natural n, $\sum_{d|n} \frac{\mu(d)}{d}=\prod_{p|n}(1-\frac{1}{p})$
negative_passages.docid: 925
negative_passages.text: Prove that $F_n={n-1 \choose 0 }+{n-2 \choose 1 }+{n-3 \choose 2 }+\ldots$ where $F(n)$ is the $n$-th fibonacci number
negative_passages.docid: 133884
negative_passages.text: A proof using Yoneda lemma
negative_passages.docid: 144890
negative_passages.text: Recurrence $f_{n+2}=af_{n+1}+bf_n$