query: Is there a positive integer $N$ that fits?
positive_passages.docid: 1001
positive_passages.text: Number of integer solutions of $x^2 + y^2 = k$
negative_passages.docid: 981
negative_passages.text: If $n^c\in\mathbb N$ for every $n\in\mathbb N$, then $c$ is a non-negative integer?
negative_passages.docid: 67208
negative_passages.text: Can we say that there exist an integer $n$ such $A+nB$ invertible?
negative_passages.docid: 153186
negative_passages.text: Positive integer type
negative_passages.docid: 45939
negative_passages.text: For which $n≥2$ does there exist $\sigma\in A_n$ with $|\sigma| > n$
negative_passages.docid: 93572
negative_passages.text: How to determine if $n (n \geq 2)$ given numbers can be summed up to a certain number?
negative_passages.docid: 51191
negative_passages.text: Does a negative number really exist?
negative_passages.docid: 148906
negative_passages.text: Finding integers $m,n$ such that $(m-n)^2=4mn/(m+n-1)$
negative_passages.docid: 141073
negative_passages.text: Are there fewer positive integers than all integers?
negative_passages.docid: 39993
negative_passages.text: Count the number of positive solutions for a linear diophantine equation
negative_passages.docid: 122914
negative_passages.text: An integer $n$, such that $nx = 0$, where $x$ belongs to the quotient group $\Bbb Q/\Bbb Z$
negative_passages.docid: 146439
negative_passages.text: Is every sufficiently large positive integer of the form $ab + ac + bc + 1$?
negative_passages.docid: 8034
negative_passages.text: Can $n!$ be a perfect square when $n$ is an integer greater than $1$?
negative_passages.docid: 44577
negative_passages.text: Finding a formula to sum natural numbers up to $n$
negative_passages.docid: 116540
negative_passages.text: Positive integers less than 1000 without repeated digits
negative_passages.docid: 109305
negative_passages.text: Non-existence of natural numbers such that $\sqrt{n} +\sqrt{n+1} <\sqrt{x} +\sqrt{y} <\sqrt{4n+2}$
negative_passages.docid: 2402
negative_passages.text: Does $\sin n$ have a maximum value for natural number $n$?