query: What are integers $x$ and $n$ such as $ x^4+x^3+x^2+x+1 = n^2$?
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: 13120
negative_passages.text: Find all integer solutions to $x^2+y^2+z^2=2xyz$
negative_passages.docid: 33314
negative_passages.text: How many non-negative integer solutions does $x_1+x_2+\cdots+x_n=A$ have?
negative_passages.docid: 33184
negative_passages.text: Something strange about $\sqrt{ 4+ \sqrt{ 4 + \sqrt{ 4-x}}}=x$ and its friends
negative_passages.docid: 41486
negative_passages.text: If $x^n + a_{n-1}x^{n-1} + ... + a_0 = 0$ has a rational root, then such root is an integer
negative_passages.docid: 128387
negative_passages.text: Given that $a+b\sqrt[3]{2} +c\sqrt[3]{4} =0$, where $a,b,c$ are integers. Show $a=b=c=0$
negative_passages.docid: 101351
negative_passages.text: Calculate $\int \limits {x^n \over 1+x+\frac{x^2}{2!}+\frac{x^3}{3!}+...+\frac{x^n}{n!}} dx$ where $n$ is a positive integer.
negative_passages.docid: 4194
negative_passages.text: Which integers can be expressed as a sum of squares of two coprime integers?
negative_passages.docid: 136933
negative_passages.text: Which $n$ can be expressed as $x^2 − y^2$?
negative_passages.docid: 12967
negative_passages.text: Find all $n>1$ such that $\dfrac{2^n+1}{n^2}$ is an integer.
negative_passages.docid: 82571
negative_passages.text: Number of solutions of $x^2=1$ in $\mathbb{Z}/n\mathbb{Z}$
negative_passages.docid: 114185
negative_passages.text: Existence of $x$ such that $2^x =a,3^x=b,5^x=c$ for some integers $a,b,c$
negative_passages.docid: 46606
negative_passages.text: Can an integer of the form $4n+3$ written as a sum of two squares?
negative_passages.docid: 158563
negative_passages.text: If $m^4+4^n$ is prime, then $m=n=1$ or $m$ is odd and $n$ even
negative_passages.docid: 1001
negative_passages.text: Number of integer solutions of $x^2 + y^2 = k$
negative_passages.docid: 113250
negative_passages.text: If $x+{1\over x} = r $ then what is $x^3+{1\over x^3}$?
negative_passages.docid: 96185
negative_passages.text: Solutions of $x^2+y^2+z^2 = n$ in $\mathbb{Z}_2$.