query: Solve $y^3=x^{3}+8x^{2}-6x+8$ for positive integers $x, y $
positive_passages.docid: 149254
positive_passages.text: Solving $y^3=x^3+8x^2-6x+8$
negative_passages.docid: 6595
negative_passages.text: Solve for positive integers: $\frac{4}{13}=\frac{1}{x}+\frac{1}{y}+\frac{1}{z}$
negative_passages.docid: 7279
negative_passages.text: $|2^x-3^y|=1$ has only three natural pairs as solutions
negative_passages.docid: 154829
negative_passages.text: How to solve $y'' + y = y^{-3}$
negative_passages.docid: 148570
negative_passages.text: Find the all possible real solutions of $x^y=y^x$
negative_passages.docid: 68164
negative_passages.text: $(2x^2+3y^2-7)xdx-(3x^2+2y^2-8)ydy=0$
negative_passages.docid: 49794
negative_passages.text: Solve $f(x^2+y+f(y))=2y+f(x)^2$ over $\mathbb{R}$
negative_passages.docid: 118197
negative_passages.text: Solve $n(n+1)(n+2)=6m^3$ in positive integers
negative_passages.docid: 47809
negative_passages.text: If $x,y\in\mathbb Z$, solve $x^2+xy+y^2=x^2y^2$.
negative_passages.docid: 38849
negative_passages.text: Solve $x^y \, = \, y^x$
negative_passages.docid: 67015
negative_passages.text: Solve $x^2 + 8 = 3^n$, where $x\in\mathbb N$.
negative_passages.docid: 8504
negative_passages.text: Factoring $x^n + y^n$ over the integers
negative_passages.docid: 62980
negative_passages.text: How do you factorise $x^3z - x^3y - y^3z + yz^3 + xy^3 - xz^3$?
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: 28274
negative_passages.text: Prove that $x^2 + y^2 = 3(z^2 + m^2)$ has no solutions in integer
negative_passages.docid: 61877
negative_passages.text: Find all integer solutions to Diophantine equation $x^3+y^3+z^3=w^3$
negative_passages.docid: 95490
negative_passages.text: What are the positive integer solutions to $x^2-x+1 = y^3$?