query: Diophantine solutions to $x^y-y^x=1$
positive_passages.docid: 155757
positive_passages.text: Number theory: $x^y + 1 = y^x$
negative_passages.docid: 73160
negative_passages.text: Solving the Diophantine Equation $x^2 - y! = 2001$ and $x^2 - y! = 2016$
negative_passages.docid: 89804
negative_passages.text: Diophantine equation: $7^x=3^y-2$
negative_passages.docid: 80058
negative_passages.text: Three variable, third degree Diophantine equation
negative_passages.docid: 94327
negative_passages.text: Cubic Diophantine with two variables
negative_passages.docid: 142725
negative_passages.text: The general solution of $x^a = a^x$ for real $a >0$
negative_passages.docid: 135087
negative_passages.text: Find integer solutions of $xy=-1$ (using only elementary ring theory).
negative_passages.docid: 10753
negative_passages.text: Natural number solutions to $\frac{xy}{x+y}=n$ (equivalent to $\frac 1x+\frac 1y=\frac 1n$)
negative_passages.docid: 82571
negative_passages.text: Number of solutions of $x^2=1$ in $\mathbb{Z}/n\mathbb{Z}$
negative_passages.docid: 34435
negative_passages.text: Integral solutions to $y^{2}=x^{3}-1$
negative_passages.docid: 53503
negative_passages.text: Solving the diophantine equation $y^{2}=x^{3}-2$
negative_passages.docid: 1001
negative_passages.text: Number of integer solutions of $x^2 + y^2 = k$
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: 61022
negative_passages.text: Diophantine Equations : Solving $a^2+ b^2=2c^2$
negative_passages.docid: 62161
negative_passages.text: Solutions of the Pell-type equation $x^2-2y^2=-1$
negative_passages.docid: 112390
negative_passages.text: Solutions of $x^2 \equiv 1 \pmod N$
negative_passages.docid: 20834
negative_passages.text: Integer solutions to $c=a^2-b^2$