query: Solving $p^2=2xq^2+2yq+1$
positive_passages.docid: 946
positive_passages.text: How to find solutions of linear Diophantine ax + by = c?
negative_passages.docid: 124073
negative_passages.text: solving for one solution to a system of polynomials
negative_passages.docid: 102860
negative_passages.text: solve $3x^2 + 6x +1 \equiv 0 \pmod {19}$
negative_passages.docid: 103276
negative_passages.text: Solving an equation over the reals: $ x^3 + 1 = 2\sqrt[3]{{2x - 1}}$
negative_passages.docid: 115244
negative_passages.text: Integer solutions of $m^2+(m+1)^2=n^4+(n+1)^4$
negative_passages.docid: 146753
negative_passages.text: Find $x$ such that $(x^2 + 4x + 3)^x + (2x + 4)^x = (x^2 + 4x + 5)^x$
negative_passages.docid: 147442
negative_passages.text: Quadratic Diophantine Equation $x^2 + axy + y^2 = z^2$
negative_passages.docid: 103993
negative_passages.text: Find all real solutions for $x$ in $2(2^x−1)x^2+(2^{x^2}−2)x=2^{x+1}−2$.
negative_passages.docid: 123867
negative_passages.text: Solve $(a + b\sin(x))\sin(x) = p$ for $x$
negative_passages.docid: 70147
negative_passages.text: Solving $x^4 -10x^3 + 26x^2 -10x +1 = 0$.
negative_passages.docid: 69234
negative_passages.text: Solving Diophantine equation $1/x^2+1/y^2=1/z^2$
negative_passages.docid: 90261
negative_passages.text: Find all solutions of the equation $n^m=x^2+py^2$ which satisfy the following properties
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: 157264
negative_passages.text: Solve $\frac1x+\frac1y=\frac1{pq}$
negative_passages.docid: 124581
negative_passages.text: Solving $x^2 - 1 = e^x$
negative_passages.docid: 20491
negative_passages.text: How to solve this equation $x^{2}=2^{x}$?
negative_passages.docid: 35504
negative_passages.text: The Diophantine equation $x^2 + 2 = y^3$