Can you factor out a common divisor when finding $\gcd(a,b)$?
49109
Proving $\gcd \left(\frac{a}{\gcd (a,b)},\frac{b}{\gcd (a,b)}\right)=1$
73391
Prove that if $\gcd(a,b)=1$, then $\gcd(a^2,b^2)=1$
52546
How can I find the possible values that $\gcd(a+b,a^2+b^2)$ can take, if $\gcd(a,b)=1$
10348
Prove that if the $\gcd(a,b)=1$, then $\gcd(a+b,ab)=1$
111555
Find $a,b \in \mathbb{N}$ with $\mathrm{lcm}(a,b)=12\gcd(a,b)\,$ and $\,a\bmod b = 5$
18772
If $a,b \in\mathbb N$ and $\gcd(a,b)=1$, prove that $\gcd(a+b;a^2+b^2)= 1$ or $2$.
125737
GCD( LCM(a,b) , LCM(a,c) ) = LCM(b, GCD(b,c)) , why?
1197
Finding $\gcd(2n-1,2n+1)$ . . . I think it's 1 but is my logic right?
31465
Prove that if $a \mid b$ then $\gcd(a,b) = |a|$
18714
$\gcd\left(a+b,\frac{a^p+b^p}{a+b}\right)=1$, or $p$
41295
Divisibility, LCM and GCD for fractions (rationals)
113641
Suppose the gcd (a,b) = 1 and c divides a + b. Prove that gcd (a,c) = 1 = gcd (b,c)
80148
Prove $\gcd(a+b,a^2+b^2)$ is $1$ or $2$ if $\gcd(a,b) = 1$
66748
Show that if $a \equiv b \pmod n$, $\gcd(a,n)=\gcd(b,n)$
157508
prove $lcm(a,gcd(b,c))=gcd(lcm(a,b),lcm(a,c))$
85688
How to show $\gcd(ac, bd) = \gcd(a,d) * \gcd(b,c)$
151434
If integers $a$ and $b$ are not both zero, then $\gcd(a,b)=\gcd(a-b,b)$