gcd of $(2^{2^m} + 1 , 2^{2^n}+1) = 1$ for distinct pair of positive integers $n,m$
19164
On the GCD of a Pair of Fermat Numbers
23590
Show that $\gcd\left(\frac{a^n-b^n}{a-b},a-b\right)=\gcd(n d^{n-1},a-b)$
83307
If $n\mid a^2-1$, $n$ an odd integer, show $n = \gcd(a-1, n)\gcd(a+1, n)$
108450
Prove that $\gcd(a, b) = \gcd(a, b + ma)$?
55441
Check: For the integers $a,b,c$ show that $\gcd(a,bc)=\gcd(a,\gcd(a,b)\cdot c)$
112486
Bounds on a sum of gcd's
76507
$\gcd(b^x - 1, b^y - 1, b^ z- 1,\dots) = b^{\gcd(x, y, z,\dots)} -1$
31331
$|a|=m,\,\gcd(m,n)=1 \implies a$ is an $n$'th power
69279
If $\gcd(a,b)=1$ then, $\gcd(a^2,b^2)=1$
137369
Inductive proof of gcd Bezout identity (from Apostol: Math, Analysis 2ed)
97196
$k^{\phi(l)} + l^{\phi(k)} \equiv1\pmod{lk}\,$ if $\,\gcd(l,k)=1$
18772
If $a,b \in\mathbb N$ and $\gcd(a,b)=1$, prove that $\gcd(a+b;a^2+b^2)= 1$ or $2$.
129238
Divisibility of $2^n - 1$ by $2^{m+n} - 3^m$.
126280
In a P.I.D., if $a^m = b^m$ and $a^n = b^n$ for $m, n \in \mathbb{N}$ with $\gcd(m,n) = 1$, then $a=b$
156641
Show that $\gcd(3n,3n+ 2) = 1$ when $n$ is odd
56423
gcd of power plus one
1713
number theory $\gcd(a,bc)=\gcd(a,c)$