query: $x+\frac{1}{x}$ is an integer
positive_passages.docid: 49372
positive_passages.text: $x+1/x$ an integer implies $x^n+1/x^n$ an integer
negative_passages.docid: 45872
negative_passages.text: Integration: $\int\frac{1}{(x^2+x+1)^{1/2}} dx$
negative_passages.docid: 56315
negative_passages.text: Prove $\frac{|a+b|}{1+|a+b|}<\frac{|a|}{1+|a|}+\frac{|b|}{1+|b|}$.
negative_passages.docid: 112171
negative_passages.text: Proposition: $\sqrt{x + \sqrt{x + \sqrt{x + ...}}} = \frac{1 + \sqrt{1 + 4x}}{2}$.
negative_passages.docid: 58240
negative_passages.text: Find the expected value of $\frac{1}{X+1}$ where $X$ is binomial
negative_passages.docid: 144836
negative_passages.text: How to prove that $\frac{(mn)!}{m!(n!)^m}$ is an integer?
negative_passages.docid: 112907
negative_passages.text: Math Induction Proof: $(1+\frac1n)^n < n$
negative_passages.docid: 49851
negative_passages.text: when the sum of some fractions be $1$
negative_passages.docid: 104512
negative_passages.text: Why is $\frac{1}{2\pi i}\int_{\gamma}\frac{f'(z)}{f(z)}dz$ an integer?
negative_passages.docid: 104094
negative_passages.text: Integral of $\frac{1}{(1+x^2)^2}$
negative_passages.docid: 126959
negative_passages.text: Prove $ \frac{1}{x+1} \le \ln(1+\frac{1}{x}) \le \frac{1}{x}$ with usage of the definition of a logarithmic function
negative_passages.docid: 38515
negative_passages.text: Integral of $\frac{1}{x^4+1}$
negative_passages.docid: 7802
negative_passages.text: Showing $\prod\limits_{i<j} \frac{x_i-x_j}{i-j}$ is an integer
negative_passages.docid: 126852
negative_passages.text: Evaluate $\int \frac{1}{\sin x+\sec x}\,dx $
negative_passages.docid: 41141
negative_passages.text: Proving that $\frac{\phi^{400}+1}{\phi^{200}}$ is an integer.
negative_passages.docid: 14815
negative_passages.text: How prove this $\prod_{1\le i<j\le n}\frac{a_{j}-a_{i}}{j-i}$ is integer
negative_passages.docid: 146770
negative_passages.text: Why is $\frac{1}{\frac{1}{0}}$ undefined?