If $a^{-1}b^2a=b^3$ and $b^{-1}a^2b=a^3$ then $a=b=e$
8483
A Particular Two-Variable System in a Group
116616
Could $X^3 + X + 1$ have a root in $E?$
19940
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?
87397
Show that $a^2 \bmod b = (a \bmod b)^2 \bmod b$
6169
If $ A^3=A$ prove that $Ker\left(A-I\right)+Im\left(A-I\right)=V$
98470
If $A \ne \varnothing$, then $\varnothing^A=\varnothing$
136185
How $a^{\log_b x} = x^{\log_b a}$?
119156
$(a,b)=d \overset{?}{\implies} (a^3,b^3)=d^3$
15626
Relations of a~b iff b = ak^2
66558
Find the value of $a$ and $b$ if $x+1$ and $x−2$ are factors of $ax^3−4x^2+bx−12$
52658
What are the integer solutions to $a^{b^2} = b^a$ with $a, b \ge 2$
142263
Assuming $ab^2 = b^3a$ and $a^2=1$ prove that the order of $b$ is $5$.
41977
If $G$ is a group, show that $x^2ax=a^{-1}$ has a solution if and only if $a$ is a cube in $G$
127891
If $ a^{2} + b^{2} = c^{2}$ and $c$ is even, prove that $a$ and $b$ are both even.
36602
$a^m=b^m$ and $a^n=b^n$ imply $a=b$
5729
If $a^2+b^2+c^2=1$ then prove the following.
69874
Are there any integer solutions to $a^3=b^2$?