query: Given that $\frac{2^n +1}{n^2}$ is a integer.Find $n$
positive_passages.docid: 12967
positive_passages.text: Find all $n>1$ such that $\dfrac{2^n+1}{n^2}$ is an integer.
negative_passages.docid: 84147
negative_passages.text: Evaluating $\sum_{n=1}^\infty \frac{2^{2n-1}}{5^{n+1}}$
negative_passages.docid: 14223
negative_passages.text: Find the infinite sum $\sum_{n=1}^{\infty}\frac{1}{2^n-1}$
negative_passages.docid: 29170
negative_passages.text: Find the sum of the series $\sum \frac{1}{n(n+1)(n+2)}$
negative_passages.docid: 110695
negative_passages.text: Divisor of $2^{2^n} + 1$ modulus $2^{n+1}$
negative_passages.docid: 102334
negative_passages.text: How can you prove $\frac{n(n+1)(2n+1)}{6}+(n+1)^2= \frac{(n+1)(n+2)(2n+3)}{6}$ without much effort?
negative_passages.docid: 68400
negative_passages.text: Proof that $\frac{(2n)!}{2^n}$ is integer
negative_passages.docid: 112575
negative_passages.text: Finding integer solutions of $m^2-n^5 = m - n$
negative_passages.docid: 89728
negative_passages.text: Prove that $1<\frac{1}{n+1}+\frac{1}{n+2}+...+\frac{1}{3n+1}$
negative_passages.docid: 142132
negative_passages.text: How do you prove $\sum \frac {n}{2^n} = 2$?
negative_passages.docid: 100401
negative_passages.text: Evaluate $\int \frac{1}{(x^2+1)^2}dx$
negative_passages.docid: 118456
negative_passages.text: Find $\sum_{n=1}^{\infty}\tan^{-1}\frac{2}{n^2}$
negative_passages.docid: 28378
negative_passages.text: Find the infinite sum of the series $\sum_{n=1}^\infty \frac{1}{n^2 +1}$
negative_passages.docid: 46668
negative_passages.text: How to find integer solutions to $M^2=5N^2+2N+1$?
negative_passages.docid: 113336
negative_passages.text: Limit of $(\frac{1}{n^2})^{(\frac{1}{n})}$
negative_passages.docid: 155353
negative_passages.text: Find the limit of $ a_n =\left(1+\frac{1^2}{n^2}\right)^1\left(1+\frac{2^2}{n^2}\right)^2\cdots \left(1+\frac{n^2}{n^2}\right)^n$
negative_passages.docid: 156376
negative_passages.text: Find the values of $n$ that make the fraction $\frac{2n^{7}+1}{3n^{3}+2}$ reducible.