query: Find all solutions to $a^b = b^a$
positive_passages.docid: 5595
positive_passages.text: $x^y = y^x$ for integers $x$ and $y$
negative_passages.docid: 8676
negative_passages.text: Is there any "superlogarithm" or something to solve $x^x$?
negative_passages.docid: 41890
negative_passages.text: How to get all solutions of $x^2 \equiv$ $a$ mod $p$?
negative_passages.docid: 82137
negative_passages.text: Given a, b How many solutions exists for x, such that: $a \bmod{x}=b $
negative_passages.docid: 142725
negative_passages.text: The general solution of $x^a = a^x$ for real $a >0$
negative_passages.docid: 61022
negative_passages.text: Diophantine Equations : Solving $a^2+ b^2=2c^2$
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: 131941
negative_passages.text: Solve quadratic congruences.
negative_passages.docid: 124073
negative_passages.text: solving for one solution to a system of polynomials
negative_passages.docid: 79
negative_passages.text: Find $a$, $b$ and $c$ that satisfy the following equations
negative_passages.docid: 41977
negative_passages.text: If $G$ is a group, show that $x^2ax=a^{-1}$ has a solution if and only if $a$ is a cube in $G$
negative_passages.docid: 20491
negative_passages.text: How to solve this equation $x^{2}=2^{x}$?
negative_passages.docid: 86841
negative_passages.text: Find a matrix $B$ such that $B^3 = A$
negative_passages.docid: 7622
negative_passages.text: $AB-BA=I$ having no solutions
negative_passages.docid: 69874
negative_passages.text: Are there any integer solutions to $a^3=b^2$?
negative_passages.docid: 59196
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: 133925
negative_passages.text: Find All Solutions to System of Congruence