query: Solutions for $a^b = b^a$?
positive_passages.docid: 148570
positive_passages.text: Find the all possible real solutions of $x^y=y^x$
negative_passages.docid: 55100
negative_passages.text: The positive integer solutions for $2^a+3^b=5^c$
negative_passages.docid: 60006
negative_passages.text: Matrix equation: $A−A(A + B)^{−1}A = B−B(A + B)^{−1}B$
negative_passages.docid: 29462
negative_passages.text: Suggestions on how to prove the following equality. $a^{m+n}=a^m a^n$
negative_passages.docid: 87397
negative_passages.text: Show that $a^2 \bmod b = (a \bmod b)^2 \bmod b$
negative_passages.docid: 78736
negative_passages.text: Check my proof that $(ab)^{-1} = b^{-1} a^{-1}$
negative_passages.docid: 24307
negative_passages.text: Is $x^x=y$ solvable for $x$?
negative_passages.docid: 48211
negative_passages.text: When is $(a+b)^n \equiv a^n+b^n$?
negative_passages.docid: 114185
negative_passages.text: Existence of $x$ such that $2^x =a,3^x=b,5^x=c$ for some integers $a,b,c$
negative_passages.docid: 130281
negative_passages.text: Proving $a^ab^b + a^bb^a \le 1$, given $a + b = 1$
negative_passages.docid: 156541
negative_passages.text: $a^b > b^a$ or $a^b b$ where $a,b$ are positive real numbers
negative_passages.docid: 18203
negative_passages.text: Diophantine equation $a^2+b^2=c^2+d^2$
negative_passages.docid: 129454
negative_passages.text: Solution to a quadratic form
negative_passages.docid: 20110
negative_passages.text: How to prove $(AB)^T=B^T A^T$
negative_passages.docid: 20834
negative_passages.text: Integer solutions to $c=a^2-b^2$
negative_passages.docid: 144067
negative_passages.text: calculating $a^b \!\mod c$
negative_passages.docid: 136185
negative_passages.text: How $a^{\log_b x} = x^{\log_b a}$?