query: Let $A_1 A_2 \dotsb A_{11}$ be a regular 11-gon inscribed in a circle of radius 2.
positive_passages.docid: 17390
positive_passages.text: Find $LK_1^2 + LK_2^2 + \dots + LK_{11}^2$.
negative_passages.docid: 56320
negative_passages.text: Prove that the circumradius of $\triangle PAB$ is constant
negative_passages.docid: 15191
negative_passages.text: If $a^2$ divides $b^2$, then $a$ divides $b$
negative_passages.docid: 131212
negative_passages.text: Prove that if $A$ is regular then $\operatorname{adj}(\operatorname{adj}(A)) = (\det A)^{n-2} A$
negative_passages.docid: 35660
negative_passages.text: Elements of order 2 in $D_{2n}$
negative_passages.docid: 69352
negative_passages.text: Prove that $I= \{a+bi \in ℤ[i] : a≡b \pmod{2}\}$ is an maximal ideal of $ℤ[i]$.
negative_passages.docid: 115733
negative_passages.text: Proving that $\sec\frac{\pi}{11}\sec\frac{2\pi}{11}\sec\frac{3\pi}{11}\sec\frac{4\pi}{11}\sec\frac{5\pi}{11}=32$
negative_passages.docid: 118574
negative_passages.text: prove that $24 \mid a(a^2-1)$
negative_passages.docid: 40763
negative_passages.text: Possible orders of permutations of $11$ symbols
negative_passages.docid: 137186
negative_passages.text: Let G be $\mathbb Z_p\times\dots\times \mathbb Z_p$ . Find A(G).
negative_passages.docid: 9149
negative_passages.text: Any $B \subset \{10,11,...,99\}$, with $|B| =10$ has two subsets such that $\sum_{a \in B_1} a = \sum_{b \in B_2} b$
negative_passages.docid: 150064
negative_passages.text: Cardinality of "$x-y\in\Bbb Q$"-equivalence class of $1/\sqrt2$
negative_passages.docid: 34954
negative_passages.text: If $11..11$($n$ times 1) is prime, prove that $n$ is also prime
negative_passages.docid: 68771
negative_passages.text: Assume that $ 1a_1+2a_2+\cdots+na_n=1$, where the $a_j$ are real numbers.
negative_passages.docid: 46106
negative_passages.text: Prove that $D_r \circ D_s = \{ (x,y) \in \mathbb{R}^2 \ | \ |x-y|<r+s \}$, where $D_a = \{ (x,y) \in \mathbb{R}^2\ | \ |x-y| < a \}$
negative_passages.docid: 6837
negative_passages.text: How to quotient $\mathbb Z [\sqrt{-11}] / (1+\sqrt{-11})$?
negative_passages.docid: 67313
negative_passages.text: Proving $\{(x_1, x_2) \in \mathbb{R}^2_{+} \mid x_1 x_2 \geq 1\}$ is convex