In a ring with no zero-divisors, for $(m,n) =1$, $a^m = b^m$ and $a^n = b^n$ $\iff a =b$
36602
$a^m=b^m$ and $a^n=b^n$ imply $a=b$
95408
Give an example to show that a factor ring of a ring with divisors of 0 may be an integral domain
78852
If $\gcd(m,n) =1, $ then $m\mathbb{Z}/ mn\mathbb{Z} \cong \mathbb{Z}/(n)$
69131
Different proofs of $\,a^n-b^n =(a-b)\sum_{i=0}^{n-1} a^i b^{n-1-i} $?
151806
Prove that $A^k = 0 $ iff $A^2 = 0$
117777
What are the zero divisors of $C[0,1]$?
68807
How to show that the ring $S/A$ has no zero divisors? (Hungerford, Algebra, Problem 12, Chapter III, Section 2)
12694
Why does $a^n - b^n$ never divide $a^n + b^n$?
38549
$\mathbb{Q}(\sqrt{n}) \cong \mathbb{Q}(\sqrt{m})$ iff $n=m$
115782
Proof $\mathbb{A}^n$ is irreducible, without Nullstellensatz
125604
Proof that $\mathbb{Z}$ has no zero divisors
78678
If $\gcd(m,n)=1$, and $\gcd(a,m)=\gcd(b,n)=1$, then $\gcd(ab, mn)=1$
92583
Prove that $N(\gamma) = 1$ if, and only if, $\gamma$ is a unit in the ring $\mathbb{Z}[\sqrt{n}]$
102072
Simple $M_n(D)$-module with $D$ a division ring
154530
Rings whose elements are partitioned between units and zero-divisors.
111786
for any ring $A$ the matrix ring $M_n(A)$ is simple if and only if $A$ is simple
36862
A question about proving that there is no greatest common divisor