Prove $\gcd\left(\frac{a^m - 1}{a -1},a -1\right) = \gcd(m,a-1)$
23590
Show that $\gcd\left(\frac{a^n-b^n}{a-b},a-b\right)=\gcd(n d^{n-1},a-b)$
18714
$\gcd\left(a+b,\frac{a^p+b^p}{a+b}\right)=1$, or $p$
51858
Showing $\gcd(2^m-1,2^n+1)=1$
147902
Prove $a \mid m$ and $b \mid m \implies \frac{a \cdot b}{\text{gcd}(a, b)} \mid m$
56612
Proof of $\gcd(a,b)=ax+by\ $ [Bezout's identity]
32344
Let $a,k,m$ be integers. Prove that $\gcd(ka,km) = k\gcd(a,m)$.
21788
Proving that if $ad-bc = \pm 1$, then $\gcd(x,y) = \gcd(ax +by, cx + dy)$
78678
If $\gcd(m,n)=1$, and $\gcd(a,m)=\gcd(b,n)=1$, then $\gcd(ab, mn)=1$
77064
Proving $\gcd((a+b)^m,(a-b)^m)\le2^m$ for coprime $a,b$ and $m \in \Bbb N$
154959
Proof of associativity of GCD?
25825
Proof that $\gcd(ax+by,cx+dy)=\gcd(x,y)$ if $ad-bc= \pm 1$
37808
Show that $\gcd(a^2, b^2) = \gcd(a,b)^2$
97469
How to prove $|a^k|=n/\gcd(n,k)$ whenever $|a|=n$?
85688
How to show $\gcd(ac, bd) = \gcd(a,d) * \gcd(b,c)$
33996
Proving that $\gcd(2^m - 1, 2^n - 1) = 2^{\gcd(m,n )} - 1$
108450
Prove that $\gcd(a, b) = \gcd(a, b + ma)$?
81116
$gh = hg, \ \gcd(|g|, |h|) = 1\Rightarrow|gh| = |g||h|\ \ (|a|$ = order of element $a)$