query: Consider the following Diophantine equation: $x^2 + xy + y^2 = n$
positive_passages.docid: 152638
positive_passages.text: The set of integers $n$ expressible as $n=x^2+xy+y^2$
negative_passages.docid: 106271
negative_passages.text: Solutions of Diophantine equations in Natural numbers
negative_passages.docid: 53503
negative_passages.text: Solving the diophantine equation $y^{2}=x^{3}-2$
negative_passages.docid: 112575
negative_passages.text: Finding integer solutions of $m^2-n^5 = m - n$
negative_passages.docid: 77763
negative_passages.text: Proof that the equation $x^2 - 3y^2 = 1$ has infinite solutions for $x$ and $y$ being integers
negative_passages.docid: 62161
negative_passages.text: Solutions of the Pell-type equation $x^2-2y^2=-1$
negative_passages.docid: 23835
negative_passages.text: Discrete mathematics - Find all integer solutions of the equation $a^2+ b^2 + c^2=a^2 b^2$.
negative_passages.docid: 156468
negative_passages.text: Solutions to $a+b+c=12$, $a, b, c \in \mathbb{N}_0$
negative_passages.docid: 89804
negative_passages.text: Diophantine equation: $7^x=3^y-2$
negative_passages.docid: 65000
negative_passages.text: prove that $x^2 + y^2 = z^4$ has infinitely many solutions with $(x,y,z)=1$
negative_passages.docid: 105302
negative_passages.text: Solutions of bivariate cubic Diophantine equation
negative_passages.docid: 137015
negative_passages.text: Solutions for $a^2+b^2+c^2=d^2$
negative_passages.docid: 72023
negative_passages.text: Integer solutions of the equation $x^2+y^2+z^2 = 2xyz$
negative_passages.docid: 20834
negative_passages.text: Integer solutions to $c=a^2-b^2$
negative_passages.docid: 82931
negative_passages.text: How do I solve a linear Diophantine equation with three unknowns?
negative_passages.docid: 144863
negative_passages.text: Finding integer solutions to $y^2=x^3-2$
negative_passages.docid: 71361
negative_passages.text: Prove that $x^x+y^y=z^z$ doesn't have integer solutions