For $R=\Bbb Z/m\Bbb Z$, show $ā∈R^\times ⟺\gcd(a,m)=1⟺ā$ is not a zero divisor in $R$
33052
How to prove $\bar{m}$ is a zero divisor in $\mathbb{Z}_n$ if and only if $m,n$ are not coprime
31555
Divisor of $m$ and $n$ divides $m - qn$ (in proof of Euclidean algorithm)
10348
Prove that if the $\gcd(a,b)=1$, then $\gcd(a+b,ab)=1$
28021
Showing that these two definitions of $\gcd(a,b)$ are equivalent
51858
Showing $\gcd(2^m-1,2^n+1)=1$
77278
If $\,\gcd(a,b) = {\rm lcm}(a,b)\,$ then prove $a=b$
24845
Let $a\mid c$ and $b\mid c$ such that $\gcd(a,b)=1$, Show that $ab\mid c$
78263
Prove $GL_n(\Bbb{R})/SL_n(\Bbb{R}) \cong \Bbb{R}^\times$
37808
Show that $\gcd(a^2, b^2) = \gcd(a,b)^2$
24203
Finding Zero Divisors and Units of Rings $\mathbb{Z}_n \times \mathbb{Z}_m$
138058
Prove that $\mathbb Z_{m}\times\mathbb Z_{n} \cong \mathbb Z_{mn}$ implies $\gcd(m,n)=1$.
65218
Let $m \in \mathbb{Z^+} , n \in \mathbb{Z^+}$ and let $d=\gcd(m,n)$. Prove that $m\mathbb{Z}+n\mathbb{Z}=d\mathbb{Z}$
142693
$\gcd(a,b) = \gcd(a + b, \mathrm{lcm}[a,b])$
68807
How to show that the ring $S/A$ has no zero divisors? (Hungerford, Algebra, Problem 12, Chapter III, Section 2)
33996
Proving that $\gcd(2^m - 1, 2^n - 1) = 2^{\gcd(m,n )} - 1$
55673
Alternate proof that $\exists\ x \in \Bbb{Z}$ such that $ \gcd (a+bx,c) = 1$?
77064
Proving $\gcd((a+b)^m,(a-b)^m)\le2^m$ for coprime $a,b$ and $m \in \Bbb N$