Does $a^n=b^n$ and $a^m = b^m$ implies $a=b$ in an integral domain?
36602
$a^m=b^m$ and $a^n=b^n$ imply $a=b$
19822
For $D$ a GCD domain , let $a,b,x \in D \setminus \{0\}$ , then is it true that $\gcd (ax,bx)=x \cdot \gcd (a,b)$?
13174
Show that $A[X]/(aX+b)$ is an integral domain
150958
Group theory question. If $m$ and $n$ are relatively prime, and $a$, $b$ belong to group and $a^m = b^m$ and $a^n = b^n$, how would one prove $a = b$?
26011
To show that $2$ | $x^{2n} - x^n$, $n \in \mathbb{Z^+}$ is the following adequate?
8317
Understanding a proof of "If $R$ is an integral domain, then $R[x]$ is an integral domain as well".
83938
If$(ab)^n=a^nb^n$ & $(|G|, n(n-1))=1$ then $G$ is abelian
31331
$|a|=m,\,\gcd(m,n)=1 \implies a$ is an $n$'th power
10236
Show that $a^n \mid b^n$ implies $a \mid b$
49166
$R^n \cong R^m$ iff $n=m$
43246
Showing that if $a<b$, then $a^{1/n} < b^{1/n}$
17176
Proof that $x^n \mod b = (x \mod b)^n$
59442
Are there $a,b>1$ with $a^4\equiv 1 \pmod{b^2}$ and $b^4\equiv1 \pmod{a^2}$?
123275
Prove $[A,B^n] = nB^{n-1}[A,B]$
146093
Why if $n \mid m$, then $(a^n-1) \mid (a^m-1)$?
16109
Prove that $ \int _a^b\:f\left(x\right)\:\:dx\:=\:\int _a^b\:f\left(a+b-x\right)\:\:dx $
93118
How to show that if two integral domains are isomorphic, then their corresponding field of quotients are isomorphic?