query: Why is $n_1 \sqrt{2} +n_2 \sqrt{3} + n_3 \sqrt{5} + n_4 \sqrt{7} $ never zero?
positive_passages.docid: 6869
positive_passages.text: The square roots of different primes are linearly independent over the field of rationals
negative_passages.docid: 87682
negative_passages.text: Show that $\sqrt{2}\notin \mathbb{Q}(\sqrt[4]{3})$
negative_passages.docid: 44307
negative_passages.text: Prove $\sqrt[3]{3} \notin \mathbb{Q}(\sqrt[3]{2})$
negative_passages.docid: 50930
negative_passages.text: Proving the continued fraction representation of $\sqrt{2}$
negative_passages.docid: 78351
negative_passages.text: Why is $(2, 1+\sqrt{-5})$ not principal?
negative_passages.docid: 149716
negative_passages.text: Prove that $ \sqrt{n(n+1)(n+2)(n+3)+1} $ is always a natural number
negative_passages.docid: 138501
negative_passages.text: Is $\mathbf{Q}(\sqrt{2},\sqrt{3}) = \mathbf{Q}(\sqrt{6})$?
negative_passages.docid: 137652
negative_passages.text: How many solutions does the equation $n_1 + n_2 + n_3 + n_4 + n_5 = 20$ have in the positive integers if $n_1 < n_2 < n_3 < n_4 < n_5$?
negative_passages.docid: 110195
negative_passages.text: $p=4n+3$ never has a Decomposition into $2$ Squares, right?
negative_passages.docid: 33184
negative_passages.text: Something strange about $\sqrt{ 4+ \sqrt{ 4 + \sqrt{ 4-x}}}=x$ and its friends
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: 153043
negative_passages.text: Show that $\sqrt{4+2\sqrt{3}}-\sqrt{3}$ is rational using the rational zeros theorem
negative_passages.docid: 49750
negative_passages.text: Proof of the square root inequality $2\sqrt{n+1}-2\sqrt{n}<\frac{1}{\sqrt{n}}<2\sqrt{n}-2\sqrt{n-1}$
negative_passages.docid: 39199
negative_passages.text: closed form for $\binom{n}{0}+\binom{n}{3}+\binom{n}{6}+...+\binom{n}{n}$
negative_passages.docid: 22129
negative_passages.text: Why is $\sqrt{\sum_{i=1}^n |v_i|^2} \leq \sum_{i=1}^n |v_i|$ true?
negative_passages.docid: 143409
negative_passages.text: Simplify $\sqrt {\sqrt[3]{5}-\sqrt[3]{4}}$.
negative_passages.docid: 49741
negative_passages.text: Finding a closed form for a recurrence relation $a_n=3a_{n-1}+4a_{n-2}$