query: Prove that $\sin ^{-1} 1 $ is algebraic over $\mathbb Q$
positive_passages.docid: 146047
positive_passages.text: Proving that $\cos(2\pi/n)$ is algebraic
negative_passages.docid: 90438
negative_passages.text: To prove that if $ab\equiv ac\bmod n$ and $(a,n)=1$ then $b\equiv c\bmod n$
negative_passages.docid: 63390
negative_passages.text: Infinite algebraic extensions of $\mathbb{Q}$
negative_passages.docid: 79679
negative_passages.text: Let $\alpha, \beta \in \mathbb{C}$, such that $\alpha + \beta$, and $\alpha\beta$ are algebraic. Show that $\alpha$ and $\beta$ are algebraic.
negative_passages.docid: 5069
negative_passages.text: $GL_n(\mathbb F_q)$ has an element of order $q^n-1$
negative_passages.docid: 65923
negative_passages.text: How to approach proving $f^{-1}(B\setminus C)=A\setminus f^{-1}(C)$?
negative_passages.docid: 145039
negative_passages.text: Algebraic independence over $\overline{\mathbb Q}$ and over $\mathbb Q$
negative_passages.docid: 103376
negative_passages.text: Is $\sin(p \pi/q)$ necessarily an algebraic number?
negative_passages.docid: 87848
negative_passages.text: Formal proof for $(-1) \times (-1) = 1$
negative_passages.docid: 86015
negative_passages.text: $\mathbb Q[x]/(x^2+1)$ is not isomorphic to $\mathbb Q[x]/(x^2+2)$
negative_passages.docid: 78873
negative_passages.text: How to show that the monomials are not a Schauder basis for $C[0,1]$
negative_passages.docid: 75863
negative_passages.text: how to prove $f^{-1}(B_1 \cap B_2) = f^{-1}(B_1) \cap f^{-1}(B_2)$
negative_passages.docid: 8087
negative_passages.text: Algebraic integers of $\mathbb{Q}(\sqrt{m})$ for $m$ a squarefree integer
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: 148330
negative_passages.text: Induction Proof for $F_{2n} = F^2_{n+1} - F^2_{n-1}$
negative_passages.docid: 93196
negative_passages.text: $x^4 -10x^2 +1 $ is irreducible over $\mathbb Q$
negative_passages.docid: 50266
negative_passages.text: In the following figure prove that: $AK||BC$