query: number of integral values for which $x^2+19x+92$ is a perfect square.
positive_passages.docid: 155789
positive_passages.text: Integral values of $x$ for which the expression $x^2+19x+92$ is a perfect square
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: 78593
negative_passages.text: Prove that the product of four consecutive positive integers plus one is a perfect square
negative_passages.docid: 38018
negative_passages.text: Arrangement of integers in a row such that the sum of every two adjacent numbers is a perfect square.
negative_passages.docid: 31933
negative_passages.text: $x^2 = 1$ in the ring $\mathbb{Z}/n \mathbb{Z}$
negative_passages.docid: 91560
negative_passages.text: Square Fibonacci numbers
negative_passages.docid: 103197
negative_passages.text: number of distinct solution of Integral equation
negative_passages.docid: 8034
negative_passages.text: Can $n!$ be a perfect square when $n$ is an integer greater than $1$?
negative_passages.docid: 43048
negative_passages.text: When is $2^n \pm 1$ a perfect power
negative_passages.docid: 26461
negative_passages.text: Integer solutions of $x^3-x+9=5y^2$
negative_passages.docid: 129362
negative_passages.text: The number of integral points on the hyperbola $x^2 - y^2 = (2000)^2$ is
negative_passages.docid: 44744
negative_passages.text: Integer solutions of $xy+9(x+y)=2006$
negative_passages.docid: 152638
negative_passages.text: The set of integers $n$ expressible as $n=x^2+xy+y^2$
negative_passages.docid: 5692
negative_passages.text: Proving that there is a perfect square between $n$ and $2n$
negative_passages.docid: 82571
negative_passages.text: Number of solutions of $x^2=1$ in $\mathbb{Z}/n\mathbb{Z}$
negative_passages.docid: 130499
negative_passages.text: How can $p^{q+1}+q^{p+1}$ be a perfect square?
negative_passages.docid: 101019
negative_passages.text: $x^3-9=y^2$ find integral solutions