Prove that $(ab)^\mathrm{n-1}$ = $b^\mathrm{n-1}*a^\mathrm{n-1}$ where n > 1 is a fixed integer
134403
Let $G$ be a group, and let $n\in\mathbb Z$. Show that $(ab)^n=a^nb^n\iff(ab)^{1-n}=a^{1-n}b^{1-n}$.
79219
Prove that $a^{2^n} \equiv 1 \pmod{2^{n+2}},$ where $a$ is an odd integer.
35948
How to prove $D^n/S^{n-1}\cong S^n$?
109611
If G is a group, prove that $(ab)^n =a^nb^n$ implies G is abelian.
82775
if $a>1$, Prove that $\lim a^{1\over n}=1$
83938
If$(ab)^n=a^nb^n$ & $(|G|, n(n-1))=1$ then $G$ is abelian
98855
Prove $aba^{-1}b^{-1}\in{N}$ for all $a,b$
109760
Showing that the product of all $n$th Roots of Unity is $(-1)^{n+1}$
117688
Prove that $\def\Aut{\operatorname{Aut}}\Aut(\mathbf{Z_{n}})\simeq \mathbf{Z_{n}^{*}}$
22666
Proving that if $A^n = 0$, then $I - A$ is invertible and $(I - A)^{-1} = I + A + \cdots + A^{n-1}$
52357
If $a,b \in G$, show that $ab^{n}a^{-1}=(aba^{-1})^{n}$.
11895
If $AB=0$ prove that $\mathrm{rank}(A)+\mathrm{rank}(B)\leq n$
97469
How to prove $|a^k|=n/\gcd(n,k)$ whenever $|a|=n$?
153295
Algebraic Identity $a^{n}-b^{n} = (a-b) \sum\limits_{k=0}^{n-1} a^{k}b^{n-1-k}$
63183
Suppose $a,b,m,n$ are natural numbers, prove that if $a({m \over n})=b$ and $(a,n)=1$, then ${m \over n} \in \mathbb{N}$
70827
Prove that $\sum_{i = n - b}^{a - m} {a - i \choose m}{b + i \choose n} = {a + b + 1 \choose m + n + 1}$
106584
If $A^{2n}=I$, then $A^n=\pm I$ where $A\in M_n(\mathbb{R})$