query: $\xi =e^{2*\pi/pi }$ , proof that is only two quadratic extention to $\Bbb Q $ that contained in $Q(\xi_p)$
positive_passages.docid: 53701
positive_passages.text: Unique quadratic subfield of $\mathbb{Q}(\zeta_p)$ is $\mathbb{Q}(\sqrt{p})$ if $p \equiv 1$ $(4)$, and $\mathbb{Q}(\sqrt{-p})$ if $p \equiv 3$ $(4)$
negative_passages.docid: 86454
negative_passages.text: How to prove $\cos\left(\pi\over7\right)-\cos\left({2\pi}\over7\right)+\cos\left({3\pi}\over7\right)=\cos\left({\pi}\over3 \right)$
negative_passages.docid: 28218
negative_passages.text: Elementary proof for $\sqrt[3]{xyz} \leq \dfrac{x+y+z}{3}$
negative_passages.docid: 96328
negative_passages.text: Proving $e^{i\pi} = -1$ without proving $e^{ix} = \cos x + i\sin x$
negative_passages.docid: 46353
negative_passages.text: Proof that $\cos(\pi/3)=1/2$
negative_passages.docid: 136855
negative_passages.text: Proof that $\mathbb{Z}\left[\frac{1 + \sqrt{-19}}{2}\right]$ is a PID
negative_passages.docid: 8913
negative_passages.text: Show that there is $\xi$ s.t. $f(\xi)=f\left(\xi+\frac{1}{n}\right)$
negative_passages.docid: 27086
negative_passages.text: proof for $\langle q| p \rangle = e^{ipq}$
negative_passages.docid: 125030
negative_passages.text: Prove that $\det(A)=p_1p_2-ba={bf(a)-af(b)\over b-a}$
negative_passages.docid: 67588
negative_passages.text: Why does $|e^{ix}|^2 = 1$?
negative_passages.docid: 41191
negative_passages.text: How to prove this $\pi$ formula?
negative_passages.docid: 154945
negative_passages.text: $|px^2+qx+r|\le1$ for all $x$ in $[-1; 1]$, show that $|rx^2+qx+p|\le2$ for all $x$ in $[-1; 1]$
negative_passages.docid: 146099
negative_passages.text: Why is this true: The only orthogonal projection that is also unitary from $\Bbb C^n$ to $\Bbb C^n$ is the identity
negative_passages.docid: 68065
negative_passages.text: Quadratic extensions in characteristic $2$
negative_passages.docid: 25910
negative_passages.text: Product of Quadratic Residues
negative_passages.docid: 128566
negative_passages.text: Proving $2$ generates $(\mathbb{Z}/19\mathbb{Z})^*$ by only looking at a few powers
negative_passages.docid: 126445
negative_passages.text: Proving the second root of a quadratic equation