query: Solve $a^b - b^a = 3$
positive_passages.docid: 19402
positive_passages.text: Find integral solution of $a^{b} - b^{a} = 3$
negative_passages.docid: 130281
negative_passages.text: Proving $a^ab^b + a^bb^a \le 1$, given $a + b = 1$
negative_passages.docid: 33105
negative_passages.text: Find the value of $a^2-b^2+c^2$
negative_passages.docid: 80058
negative_passages.text: Three variable, third degree Diophantine equation
negative_passages.docid: 19940
negative_passages.text: How to show that $A^3+B^3+C^3 - 3ABC = (A+B+C)(A+B\omega+C\omega^2)(A+B\omega^2+C\omega)$ indirectly?
negative_passages.docid: 11857
negative_passages.text: $A$ be a complex $3\times 3$ matrix such that $A^3=-I$
negative_passages.docid: 85297
negative_passages.text: find a $3 \times 3$ matrix $A$ such that $A \neq I_3$ and $A^{197}=I_3$.
negative_passages.docid: 69874
negative_passages.text: Are there any integer solutions to $a^3=b^2$?
negative_passages.docid: 142725
negative_passages.text: The general solution of $x^a = a^x$ for real $a >0$
negative_passages.docid: 86378
negative_passages.text: Prove that $3(a^3+b^3+c^3) > (a+b+c)(a^2+b^2+c^2)$
negative_passages.docid: 86841
negative_passages.text: Find a matrix $B$ such that $B^3 = A$
negative_passages.docid: 103274
negative_passages.text: Integer solutions to the equation $a^3+b^3+c^3=30$
negative_passages.docid: 38662
negative_passages.text: If $a,b$ are the roots of the equation $2 x^2 -3 x +1 = 0$, find an equation whose roots are $a/(2b +3)$, $b/(2a +3)$
negative_passages.docid: 111267
negative_passages.text: Prove that: $2^a+3^b<3a+4b$
negative_passages.docid: 156468
negative_passages.text: Solutions to $a+b+c=12$, $a, b, c \in \mathbb{N}_0$
negative_passages.docid: 92543
negative_passages.text: Regular expressions: Show that A*B is the solution of X = AX + B
negative_passages.docid: 156266
negative_passages.text: Solving $|x-2| + |x-5|=3$