How to find $\gcd(a^{2^m}+1,a^{2^n}+1)$ when $m \neq n$?
12862
Prove that two distinct numbers of the form $a^{2^{n}} + 1$ and $a^{2^{m}} + 1$ are relatively prime if $a$ is even and have $\gcd=2$ if $a$ is odd
53777
Why is $\gcd(x^4+1,x^2-1) = 1$ but I get $2$? [unit normalization of gcds]
80148
Prove $\gcd(a+b,a^2+b^2)$ is $1$ or $2$ if $\gcd(a,b) = 1$
38404
Prove $\gcd(a+b, a-b) = 1$ or $2\,$ if $\,\gcd(a,b) = 1$
63547
Euclid's Lemma and $\gcd(a,b)=1\Rightarrow \gcd(a^n,b^k)= 1$
7151
Let $a,m,n \in \mathbf{N}$. Show that if $\gcd(m,n)=1$, then $\gcd(a,mn)=\gcd(a,m)\cdot\gcd(a,n)$.
10348
Prove that if the $\gcd(a,b)=1$, then $\gcd(a+b,ab)=1$
110695
Divisor of $2^{2^n} + 1$ modulus $2^{n+1}$
135086
GCD of two numbers divided by their greatest common divisor is 1
73972
How to prove that $\gcd(2n^3-14n+2,n+3) = \gcd(n+3,10)$?
91506
If $\gcd(a,b) = 1$ then $\gcd(a,a + b) = 1$
18714
$\gcd\left(a+b,\frac{a^p+b^p}{a+b}\right)=1$, or $p$
142693
$\gcd(a,b) = \gcd(a + b, \mathrm{lcm}[a,b])$
130112
If $\gcd(a,n) = 1$ and $\gcd(b,n) = 1$, then $\gcd(ab,n) = 1$.
76507
$\gcd(b^x - 1, b^y - 1, b^ z- 1,\dots) = b^{\gcd(x, y, z,\dots)} -1$
136064
How can I prove that $\gcd(a,b)=1\implies \gcd(a^2,b^2)=1$ without using prime decomposition?
59006
Proof of $\gcd(n!+1, (n+1)!+1)=1$?