query: A problem with 26 distinct positive integers
positive_passages.docid: 28579
positive_passages.text: Creating a sequence that does not have an increasing or a decreasing sequence of length 3 from a set with 5 elements
negative_passages.docid: 106030
negative_passages.text: Find all the positive integer
negative_passages.docid: 28594
negative_passages.text: Number of integer solutions of the following equation
negative_passages.docid: 158124
negative_passages.text: Sum of all the positive integers problem
negative_passages.docid: 116540
negative_passages.text: Positive integers less than 1000 without repeated digits
negative_passages.docid: 53670
negative_passages.text: Prove that it is possible to choose $100$ out of the first $200$ positive integers
negative_passages.docid: 141073
negative_passages.text: Are there fewer positive integers than all integers?
negative_passages.docid: 23523
negative_passages.text: Two problems on number theory
negative_passages.docid: 96647
negative_passages.text: Number theory: Problem involving rational numbers
negative_passages.docid: 45460
negative_passages.text: Proof verification of a number theory problem involving sequences.
negative_passages.docid: 144025
negative_passages.text: Number of Solutions in this Number Puzzle
negative_passages.docid: 153241
negative_passages.text: Four different positive integers a, b, c, and d are such that $a^2 + b^2 = c^2 + d^2$
negative_passages.docid: 124488
negative_passages.text: Spivak Chapter 2, problems 27 (and 28)
negative_passages.docid: 105405
negative_passages.text: Product of three consecutive positive integers is never a perfect power
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?
negative_passages.docid: 45911
negative_passages.text: Prove that none of $\{11, 111, 1111,\dots \}$ is the perfect square of an integer
negative_passages.docid: 23427
negative_passages.text: How to prove there are no more positive integers that are products of 2 and 3 consecutive numbers?