query: For which $n$ can $\{1,2,...,n\}$ be rearranged so that the sum of each two adjacent terms is a perfect square?
positive_passages.docid: 27427
positive_passages.text: Arranging numbers from $1$ to $n$ such that the sum of every two adjacent numbers is a perfect power
negative_passages.docid: 22800
negative_passages.text: Can $\sqrt{n} + \sqrt{m}$ be rational if neither $n,m$ are perfect squares?
negative_passages.docid: 5692
negative_passages.text: Proving that there is a perfect square between $n$ and $2n$
negative_passages.docid: 108694
negative_passages.text: Efficient computation of $\sum_{i=1}^{i=\left \lfloor {\sqrt{N}} \right \rfloor}\left \lfloor \frac{N}{i^{2}} \right \rfloor$
negative_passages.docid: 34617
negative_passages.text: Number Theory: which primes are a sum of two squares?
negative_passages.docid: 69194
negative_passages.text: Partitioning sum of squares
negative_passages.docid: 75804
negative_passages.text: Is this permutation-sum problem NP-complete?
negative_passages.docid: 21000
negative_passages.text: Calculating $\sum_{k=1}^nk(k!)$ combinatorially
negative_passages.docid: 16472
negative_passages.text: Sum of First $n$ Squares Equals $\frac{n(n+1)(2n+1)}{6}$
negative_passages.docid: 22840
negative_passages.text: The sum of the first $n$ squares is a square: a system of two Pell-type-equations
negative_passages.docid: 60615
negative_passages.text: Product of $5$ consecutive integers cannot be perfect square
negative_passages.docid: 75227
negative_passages.text: If $S=\{1,2,\dots,n\}$ and $P_n(k)$ be the number of permutations of $S$ having $k$ fixed points, then $\sum_{k=0}^nk.P_{n}(k)=n!$
negative_passages.docid: 61324
negative_passages.text: Finding the "square root" of a permutation
negative_passages.docid: 72389
negative_passages.text: Positive integer $n$ such that $2n+1$ , $3n+1$ are both perfect squares
negative_passages.docid: 121036
negative_passages.text: Is there any perfect squares that are also binomial coefficients?
negative_passages.docid: 119524
negative_passages.text: For $n \in \mathbb{N}$ $\lfloor{\sqrt{n} + \sqrt{n+1}\rfloor} = \lfloor{\sqrt{4n+2}\rfloor}$
negative_passages.docid: 6204
negative_passages.text: How many permutations of $\{1, \ldots, n\}$ exist such that none of them contain $(i, i+1)$ (as a sequence) for $i \in {1,...,(n-1)}$?