query: How to solve the diophantine equation $x^y = y^x $?
positive_passages.docid: 5595
positive_passages.text: $x^y = y^x$ for integers $x$ and $y$
negative_passages.docid: 99055
negative_passages.text: How find this $x^3-5x+10=2^y$
negative_passages.docid: 113386
negative_passages.text: Find all integer roots of: $x^2(y-1)+y^2(x-1)=1$
negative_passages.docid: 147562
negative_passages.text: Sum of squares diophantine equation
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: 142313
negative_passages.text: Find all natural numbers $x,y$ such that $3^x=2y^2+1$.
negative_passages.docid: 8504
negative_passages.text: Factoring $x^n + y^n$ over the integers
negative_passages.docid: 124581
negative_passages.text: Solving $x^2 - 1 = e^x$
negative_passages.docid: 82931
negative_passages.text: How do I solve a linear Diophantine equation with three unknowns?
negative_passages.docid: 73160
negative_passages.text: Solving the Diophantine Equation $x^2 - y! = 2001$ and $x^2 - y! = 2016$
negative_passages.docid: 38636
negative_passages.text: A basic question about exponentiation: when is $a^{xy}=(a^x)^y$?
negative_passages.docid: 18903
negative_passages.text: Finding solutions to equation of the form $1+x+x^{2} + \cdots + x^{m} = y^{n}$
negative_passages.docid: 87665
negative_passages.text: Proving $x^n - y^n = (x-y)(x^{n-1} + x^{n-2} y + ... + x y^{n-2} + y^{n-1})$
negative_passages.docid: 158933
negative_passages.text: Rational solutions of $y^2 = x^3 - x$
negative_passages.docid: 38849
negative_passages.text: Solve $x^y \, = \, y^x$
negative_passages.docid: 103304
negative_passages.text: Finding the number of solutions to a diophantine equation
negative_passages.docid: 63194
negative_passages.text: Find all integer solutions to $x^2-2y^2=1$