query: Find all the ordered pairs $(x,y)$ such that $x^y=y^x$
positive_passages.docid: 5595
positive_passages.text: $x^y = y^x$ for integers $x$ and $y$
negative_passages.docid: 74827
negative_passages.text: Integer ordered pair of $(x,y)$ in complex algebraic equation
negative_passages.docid: 39894
negative_passages.text: Graphing y=x^2 and y=x
negative_passages.docid: 29811
negative_passages.text: Find all polynomials $P$ such that $P(x^2+1)=P(x)^2+1$
negative_passages.docid: 131414
negative_passages.text: How to get a list of pairs into the form $(x,y)$?
negative_passages.docid: 83386
negative_passages.text: Inequality with exponents $x^x+y^y \ge x^y +y^x$
negative_passages.docid: 25078
negative_passages.text: What is the solution set for the equation$ x ^ y = y ^ x$ in positive real numbers, x not equal to y?
negative_passages.docid: 15268
negative_passages.text: Find all $x,y \in \mathbb N^*$ such that $\frac{1}{x} + \frac{1}{y}=5$
negative_passages.docid: 35066
negative_passages.text: Nature and number of solutions to $xy=x+y$
negative_passages.docid: 33332
negative_passages.text: A classic exponential inequality: $x^y+y^x>1$
negative_passages.docid: 127183
negative_passages.text: Proof: For all integers $x$ and $y$, if $x^3+x = y^3+y$ then $x = y$
negative_passages.docid: 144821
negative_passages.text: Number of ordered pairs of subsets
negative_passages.docid: 76507
negative_passages.text: $\gcd(b^x - 1, b^y - 1, b^ z- 1,\dots) = b^{\gcd(x, y, z,\dots)} -1$
negative_passages.docid: 22482
negative_passages.text: How can an ordered pair be expressed as a set?
negative_passages.docid: 147892
negative_passages.text: Proving if $x<y$ then $\sqrt{x} < \sqrt{y}$
negative_passages.docid: 37976
negative_passages.text: Find all functions $f$ such that $(x+y)f(x)+f(y^2)=(x+y)f(y)+f(x^2)$
negative_passages.docid: 18761
negative_passages.text: Given that $x^y=y^x$, what could $x$ and $y$ be?