If $GCD(a,b)=1$, then $GCD((a+b)^m , (a-b)^m )$ is at most $2^m$?
92630
How to prove $\gcd(a^m,b^m) = \gcd(a,b)^m$ using Bézout's Lemma
158308
Proving that if $a,b$ are even, then $\gcd(a,b) = 2 \gcd(a/2, b/2)$
3694
Show $GCD(a_1, a_2, a_3, \ldots , a_n)$ is the least positive integer that can be expressed in the form $a_1x_1+a_2x_2+ \ldots +a_nx_n$
19700
Prove that if $a$ and $b$ are relatively prime, then $\gcd(a+b, a-b) = 1$ or $2$
147246
If $\gcd(a,c)=1=\gcd(b,c)$, then $\gcd(ab,c)=1$
82938
$\gcd(a,b)=1, x^a = y^b\Rightarrow x = n^b$, $ y = n^a$ for an integer $n$.
77064
Proving $\gcd((a+b)^m,(a-b)^m)\le2^m$ for coprime $a,b$ and $m \in \Bbb N$
19500
How can I find $\gcd(a^m+1,a^n+1)$ with $a,m,n$ positive integers?
142693
$\gcd(a,b) = \gcd(a + b, \mathrm{lcm}[a,b])$
157784
Prove that if $\gcd(ab,c)=1$, then $\gcd(a,c)=1$.
76680
Prove that if $\gcd(a,c)=1$ and $\gcd(b,c)=1$ then $\gcd(ab,c)=1$
85688
How to show $\gcd(ac, bd) = \gcd(a,d) * \gcd(b,c)$
48839
Show that the order of $a\times b$ is equal to $nm$ if gcd(n,m)=1
57281
Is Bezout's lemma enough to confirm the GCD of a number.
34330
How to prove $\gcd(a^2,b^2) = (\gcd(a,b))^2$?
96535
Show that if $\gcd(a,3)=1$ then $a^7 \equiv a\pmod{63}$. Why is this assumption necessary?
77278
If $\,\gcd(a,b) = {\rm lcm}(a,b)\,$ then prove $a=b$