query: 30 positive integers, edited.
positive_passages.docid: 149489
positive_passages.text: 30 positive integers
negative_passages.docid: 107121
negative_passages.text: Integer solutions to combinations of floating point numbers
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: 134478
negative_passages.text: Find the highest natural number which is divisible by $30$ and has exactly $30$ different positive divisors.
negative_passages.docid: 31687
negative_passages.text: Classification of groups of order 30
negative_passages.docid: 152638
negative_passages.text: The set of integers $n$ expressible as $n=x^2+xy+y^2$
negative_passages.docid: 49366
negative_passages.text: Group of order 30 can't be simple
negative_passages.docid: 123891
negative_passages.text: There are finitely many maps on nonnegative integers satisfying $\phi(ab)=\phi(a)+\phi(b)$
negative_passages.docid: 43865
negative_passages.text: Find all positive integers $n$ such that $\phi(n)=6$.
negative_passages.docid: 134440
negative_passages.text: An unexpected application of non-trivial combinatorics
negative_passages.docid: 107964
negative_passages.text: Simple combinatorics problem.
negative_passages.docid: 146439
negative_passages.text: Is every sufficiently large positive integer of the form $ab + ac + bc + 1$?
negative_passages.docid: 121469
negative_passages.text: Proof of observations on natural numbers being expressed as differences of squares.
negative_passages.docid: 105719
negative_passages.text: Complex numbers modulo integers
negative_passages.docid: 60965
negative_passages.text: Representing a nonnegative integer as the ordered sum of odd numbers
negative_passages.docid: 65763
negative_passages.text: Number of ways to write n as a sum of k nonnegative integers
negative_passages.docid: 22367
negative_passages.text: How do I prove that for every positive integer $n$, there exist $n$ consecutive positive integers, each of which is composite?