query: How to show that $2+\sqrt{5}i\not | 3$?
positive_passages.docid: 151797
positive_passages.text: Which element belong to the principal ideal $(3+i)$?
negative_passages.docid: 126427
negative_passages.text: Proving $\sqrt{2}+\sqrt[3]{3}$ is algebraic.
negative_passages.docid: 27068
negative_passages.text: Show that $\sqrt{2+\sqrt{2+\sqrt{2...}}}$ converges to 2
negative_passages.docid: 27021
negative_passages.text: Show that $Q[\sqrt3]$ is a field
negative_passages.docid: 149675
negative_passages.text: Simplifying $\sqrt[4]{161-72 \sqrt{5}}$
negative_passages.docid: 28218
negative_passages.text: Elementary proof for $\sqrt[3]{xyz} \leq \dfrac{x+y+z}{3}$
negative_passages.docid: 56802
negative_passages.text: Why $\sqrt[3]{{2 + \sqrt 5 }} + \sqrt[3]{{2 - \sqrt 5 }}$ is a rational number?
negative_passages.docid: 114506
negative_passages.text: Expansion of $(1+\sqrt{2})^n$
negative_passages.docid: 55582
negative_passages.text: How can I show that $\sqrt{1+\sqrt{2+\sqrt{3+\sqrt\ldots}}}$ exists?
negative_passages.docid: 21972
negative_passages.text: How to show that $\sqrt{2}+\sqrt{3}$ is algebraic?
negative_passages.docid: 116054
negative_passages.text: The number $(3+\sqrt{5})^n+(3-\sqrt{5})^n$ is an integer
negative_passages.docid: 5043
negative_passages.text: Show that $2^n>1+n\sqrt{2^{n-1}}$
negative_passages.docid: 126074
negative_passages.text: Proof of the irrationality of $\sqrt{3}$ - logic question
negative_passages.docid: 21826
negative_passages.text: How to prove $\sqrt{5+\sqrt{5+\sqrt{5-\sqrt{5+\sqrt{5+\sqrt{5+\sqrt{5-\cdots}}}}}}} = \frac{2+\sqrt 5 +\sqrt{15-6\sqrt 5}}{2}$
negative_passages.docid: 137970
negative_passages.text: $2 + 2 = 5$ (Fake proof, or ?)
negative_passages.docid: 87682
negative_passages.text: Show that $\sqrt{2}\notin \mathbb{Q}(\sqrt[4]{3})$
negative_passages.docid: 41418
negative_passages.text: $2+2 = 5$? error in proof