query: There should be possibly infinite ordered triplets for the following question.
positive_passages.docid: 150909
positive_passages.text: GCD is MIN of Exponents of Prime Factors, LCM is MAX of Exponents of Prime Factors.
negative_passages.docid: 134440
negative_passages.text: An unexpected application of non-trivial combinatorics
negative_passages.docid: 91281
negative_passages.text: Proving the so-called "Well Ordering Principle"
negative_passages.docid: 38242
negative_passages.text: Explicit bijection between the successor of $\alpha$ and $\alpha$ (infinite ordinal).
negative_passages.docid: 126569
negative_passages.text: Can we find a well ordering on an infinite set with no largest element?
negative_passages.docid: 40763
negative_passages.text: Possible orders of permutations of $11$ symbols
negative_passages.docid: 35326
negative_passages.text: There are infinitely many $N$ such that $\frac{N}{2}$ is a perfect square, $\frac{N}{3}$ is a perfect cube, and $\frac{N}{5}$ is a perfect fifth power
negative_passages.docid: 63618
negative_passages.text: Can all ordinals be obtained by taking successors and countable limits?
negative_passages.docid: 154225
negative_passages.text: How many positive numbers need to be added together to ensure that the sum is infinite?
negative_passages.docid: 15885
negative_passages.text: Infinite tetration, convergence radius
negative_passages.docid: 41783
negative_passages.text: Cardinality of the Cartesian Product of Two Equinumerous Infinite Sets
negative_passages.docid: 24924
negative_passages.text: Computing an infinite product
negative_passages.docid: 72843
negative_passages.text: Parity of number of factors up to a bound?
negative_passages.docid: 48502
negative_passages.text: number of ordered pairs of integers $(x,y)$ satisfying the equation
negative_passages.docid: 71108
negative_passages.text: Is there an integer $N>0$ such that $\varphi(n) = N$ has infinitely many solutions?
negative_passages.docid: 81124
negative_passages.text: Infinite product problem: $\sum p_n0$
negative_passages.docid: 10839
negative_passages.text: Problem in Cardinality and Order