query: for which values of $n$, $1+n+n^{2}+n^{3}+n^{4}$ is a perfect square?
positive_passages.docid: 147848
positive_passages.text: Integer $x$ for which $x^4+x^3+x^2+x+1$ is perfect square.
negative_passages.docid: 132879
negative_passages.text: Matlab questions about $a_{n+1} = 4a_{n} + n +1$
negative_passages.docid: 63383
negative_passages.text: Integers $n$ for which $|2^n + 5^n – 65|$ is a perfect square
negative_passages.docid: 51518
negative_passages.text: Is $\sqrt[3]{p+q\sqrt{3}}+\sqrt[3]{p-q\sqrt{3}}=n$, $(p,q,n)\in\mathbb{N} ^3$ solvable?
negative_passages.docid: 65965
negative_passages.text: Theoretical way to prove no positive integer $n$ exists such that $n+3$ and $n^2+3n+3$ are both perfect cubes.
negative_passages.docid: 99606
negative_passages.text: Prove or disprove there exists a set of four numbers out of the $48$ positive integers of which product is a perfect square
negative_passages.docid: 72389
negative_passages.text: Positive integer $n$ such that $2n+1$ , $3n+1$ are both perfect squares
negative_passages.docid: 83862
negative_passages.text: How to prove that the number $1!+2!+3!+...+n!$ is never square?
negative_passages.docid: 55206
negative_passages.text: Prove that the equation $x^4+(2k^2)x^2+2k^4$ is not a perfect square
negative_passages.docid: 41641
negative_passages.text: $(n-7)(n+7)=$ some perfect square
negative_passages.docid: 117970
negative_passages.text: Find the minimal polynomial for $\sqrt[3]{2} + \sqrt[3]{4}$ over $\mathbb{Q}$
negative_passages.docid: 87666
negative_passages.text: Find $n$ such that $n/2$ is a square, $n/3$ is a cube, and $n/5$ a fifth power
negative_passages.docid: 118538
negative_passages.text: Find all integers $x$ such that $x^2+3x+24$ is a perfect square.
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: 99502
negative_passages.text: Question on the coefficients of $(1+x+x^2+x^3+x^4)^{496}$
negative_passages.docid: 138548
negative_passages.text: For what pair of integers $(a,b)$ is $3^a + 7^b$ a perfect square.
negative_passages.docid: 136366
negative_passages.text: Show that if $2+2\sqrt{28n^2+1}$ is an integer then it must be perfect square.