Let a, b, d be non-zero integers. If d|a and d|b, prove d|gcd(a,b)
51538
Intuition for $\,c\mid a,b \iff c\mid \gcd(a,b)$
157784
Prove that if $\gcd(ab,c)=1$, then $\gcd(a,c)=1$.
135779
Prove the following: If $a \mid bc$, then $a \mid \gcd(a, b)c$.
142693
$\gcd(a,b) = \gcd(a + b, \mathrm{lcm}[a,b])$
113641
Suppose the gcd (a,b) = 1 and c divides a + b. Prove that gcd (a,c) = 1 = gcd (b,c)
59006
Proof of $\gcd(n!+1, (n+1)!+1)=1$?
28021
Showing that these two definitions of $\gcd(a,b)$ are equivalent
69279
If $\gcd(a,b)=1$ then, $\gcd(a^2,b^2)=1$
110313
Prove that $\gcd(f(x),g(x)) = 1$.
82777
If $\gcd(a, b) = 1$ then prove that $\gcd(a+b, a^2-ab+b^2) = 1$ or $3$?
128820
Prove that if $\gcd(a,b)=1$ then $\gcd(ab,c) = \gcd(a,c) \gcd(b,c)$
7091
If $\gcd(a,b)=1$, then $\gcd(a^n,b^n)=1$
23590
Show that $\gcd\left(\frac{a^n-b^n}{a-b},a-b\right)=\gcd(n d^{n-1},a-b)$
85688
How to show $\gcd(ac, bd) = \gcd(a,d) * \gcd(b,c)$
97469
How to prove $|a^k|=n/\gcd(n,k)$ whenever $|a|=n$?
18772
If $a,b \in\mathbb N$ and $\gcd(a,b)=1$, prove that $\gcd(a+b;a^2+b^2)= 1$ or $2$.
5708
Prove that if $k\ge 1\,$ and $\,a^k\equiv 1\pmod{\! n}$ then $\gcd(a,n)=1$