query: Is $\sqrt1+\sqrt2+\dots+\sqrt n$ ever an integer?
positive_passages.docid: 24301
positive_passages.text: Can a finite sum of square roots be an integer?
negative_passages.docid: 138081
negative_passages.text: How to determine whether a number can be written as a sum of two squares?
negative_passages.docid: 11935
negative_passages.text: Is $\mathbb{Z} \left[ \frac{1+i \sqrt{7}}{2} \right]$ euclidean?
negative_passages.docid: 40525
negative_passages.text: Fastest way to determine if an integer's square root is an integer
negative_passages.docid: 112368
negative_passages.text: Is there a rule for $\sqrt{a+b}$?
negative_passages.docid: 109900
negative_passages.text: Why is $e^{\pi \sqrt{163}}$ almost an integer?
negative_passages.docid: 137010
negative_passages.text: What are integers $x$ and $n$ such as $ x^4+x^3+x^2+x+1 = n^2$?
negative_passages.docid: 50927
negative_passages.text: If $m,n\in N$ Prove that there is such a positive integer k, such that $(\sqrt{m}+\sqrt{m+1})^n=\sqrt{k}+\sqrt{k+1}$
negative_passages.docid: 13617
negative_passages.text: Evaluating the nested radical $ \sqrt{1 + 2 \sqrt{1 + 3 \sqrt{1 + \cdots}}} $.
negative_passages.docid: 115244
negative_passages.text: Integer solutions of $m^2+(m+1)^2=n^4+(n+1)^4$
negative_passages.docid: 58182
negative_passages.text: How to prove that $\mathbb{Q}[\sqrt{p_1}, \sqrt{p_2}, \ldots,\sqrt{p_n} ] = \mathbb{Q}[\sqrt{p_1}+ \sqrt{p_2}+\cdots + \sqrt{p_n}]$, for $p_i$ prime?
negative_passages.docid: 62792
negative_passages.text: Can sum of a rational number and its reciprocal be an integer?
negative_passages.docid: 22800
negative_passages.text: Can $\sqrt{n} + \sqrt{m}$ be rational if neither $n,m$ are perfect squares?
negative_passages.docid: 2776
negative_passages.text: What can be said about the integral part of $(a+\sqrt{b})^n $
negative_passages.docid: 28912
negative_passages.text: Does this series diverge: $(\sqrt 2-\sqrt 1)+(\sqrt 3-\sqrt 2)+(\sqrt 4-\sqrt 3)+(\sqrt 5-\sqrt 4)+\dots$?
negative_passages.docid: 52206
negative_passages.text: How to prove with double counting technique that $1+2+\dots+2^n=2^{n+1} -1$?
negative_passages.docid: 19676
negative_passages.text: Is it known whether ${\sqrt{2}}^{\sqrt{2}}$ is irrational?