How to solve $a^{b^2} = b^a$ in positive integers
52658
What are the integer solutions to $a^{b^2} = b^a$ with $a, b \ge 2$
91113
$ \exists a, b \in \mathbb{Z} $ such that $ a^2 + b^2 = 5^k $
15191
If $a^2$ divides $b^2$, then $a$ divides $b$
101872
Prove that $\gcd(a^2, b^2) = \gcd(a, b)^2$
18693
If $a,b$ are positive integers such that $a^{n}+n$ divides $b^{n}+n$ for every $n$, then $a=b$
19500
How can I find $\gcd(a^m+1,a^n+1)$ with $a,m,n$ positive integers?
144067
calculating $a^b \!\mod c$
18203
Diophantine equation $a^2+b^2=c^2+d^2$
30835
Logarithm proof problem: $a^{\log_b c} = c^{\log_b a}$
87029
Solve $y^2=x^3-4$ in $x,y\in \mathbb{Z}$
142725
The general solution of $x^a = a^x$ for real $a >0$
158844
If $a$ and $b$ are positive real numbers such that $a+b=1$, prove that $(a+1/a)^2+(b+1/b)^2\ge 25/2$
45090
Given any positive real numbers $a,b,c$, we have $(a^{2}+2)(b^{2}+2)(c^{2}+2)\geq 9(ab+bc+ca)$
80982
Solve $a^3+b^3+3ab=1$ with $(a,b)\in \Bbb{Z}^2$
90486
If $(A-B)^2=O_2$ then $\det(A^2 - B^2)=(\det(A) - \det(B))^2$
125057
How do I solve a problem with term $a^{n} + b^{n}$?
78736
Check my proof that $(ab)^{-1} = b^{-1} a^{-1}$