query: Find all ordered pairs $(x,y)$ of positive integers such that the expression $x^2+y^2+xy$ is a perfect square.
positive_passages.docid: 147442
positive_passages.text: Quadratic Diophantine Equation $x^2 + axy + y^2 = z^2$
negative_passages.docid: 147848
negative_passages.text: Integer $x$ for which $x^4+x^3+x^2+x+1$ is perfect square.
negative_passages.docid: 117392
negative_passages.text: Does $x^2 - y^2 = 12345678$ (x,y are integers) have any solutions?
negative_passages.docid: 21898
negative_passages.text: Find all primes $p$ such that $ p^3-4p+9 $ is a perfect square.
negative_passages.docid: 54355
negative_passages.text: $1+x+\ldots+x^n$ perfect square
negative_passages.docid: 1001
negative_passages.text: Number of integer solutions of $x^2 + y^2 = k$
negative_passages.docid: 157746
negative_passages.text: Finding all positive integer solutions to $(x!)(y!) = x!+y!+z!$
negative_passages.docid: 25784
negative_passages.text: Let $x$ and $y$ be positive integers such that $xy \mid x^2+y^2+1$.
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.
negative_passages.docid: 154082
negative_passages.text: Product of factorials divided by factorial to produce perfect square
negative_passages.docid: 72437
negative_passages.text: Sum of the digits of a perfect square
negative_passages.docid: 155363
negative_passages.text: Find all integers $(x, y)$ such that $1 + 2^x + 2^{2x + 1} = y^2$
negative_passages.docid: 105564
negative_passages.text: If $n$ is a positive integer greater than 1 such that $3n+1$ is perfect square, then show that $n+1$ is the sum of three perfect squares.
negative_passages.docid: 144863
negative_passages.text: Finding integer solutions to $y^2=x^3-2$
negative_passages.docid: 48502
negative_passages.text: number of ordered pairs of integers $(x,y)$ satisfying the equation
negative_passages.docid: 124223
negative_passages.text: Find all pairs (x, y) of real numbers such that $16^{x^2+y} + 16^{x+y^2}=1$
negative_passages.docid: 48430
negative_passages.text: Prove the following sequence always results in a perfect square.