query: Determine all integers (bigger than 1) such that $\frac{2^n+1}{n^2}$ is an integer
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: 77547
negative_passages.text: Find integers $a,b,c,d$ such that
negative_passages.docid: 85731
negative_passages.text: Prove by induction that $n! > n^2$
negative_passages.docid: 52324
negative_passages.text: Tight bound for $T(n) = T(n^{1/2}) + 1$
negative_passages.docid: 33810
negative_passages.text: Proving there are an infinite number of pairs of positive integers $(m,n)$ such that $\frac{m+1}{n}+\frac{n+1}{m}$ is a positive integer
negative_passages.docid: 119109
negative_passages.text: Integer solutions to $ n^2 + 1 = 2 \times 5^m$
negative_passages.docid: 138905
negative_passages.text: Find the limit of $\log\Big(\frac{(n^2+n)!}{n^2!n^{2n}}\Big)$
negative_passages.docid: 44790
negative_passages.text: Find $n$ for which $\frac{n(n+1)}{2}$ is perfect square
negative_passages.docid: 121554
negative_passages.text: Finding $\sum\frac{1}{2^n(n+1)}$
negative_passages.docid: 131385
negative_passages.text: How to provide a counterexample for if $n$ is prime, then $2^n -1$ is prime
negative_passages.docid: 66358
negative_passages.text: Prove by mathematical induction that $2n ≤ 2^n$, for all integer $n≥1$?
negative_passages.docid: 148647
negative_passages.text: If $\dfrac{4x^2-1}{4x^2-y^2}$ is an integer, then it is $1$
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: 145274
negative_passages.text: Prove by induction $\sum \frac {1}{2^n} < 1$
negative_passages.docid: 46668
negative_passages.text: How to find integer solutions to $M^2=5N^2+2N+1$?
negative_passages.docid: 152638
negative_passages.text: The set of integers $n$ expressible as $n=x^2+xy+y^2$
negative_passages.docid: 151153
negative_passages.text: Prove $\frac{a(a^2+2)}{3}$ is an integer for all integer $a\geqslant 1$