Prove $\gcd(a^{2^m}+1, a^{2^n}+1)$ is either $1$ or $2$
14783
A Number Theory problem (GCD)
34330
How to prove $\gcd(a^2,b^2) = (\gcd(a,b))^2$?
91506
If $\gcd(a,b) = 1$ then $\gcd(a,a + b) = 1$
2289
Prove that if $\gcd( a, b ) = 1$ then $\gcd( ac, b ) = \gcd( c, b ) $
105832
prove that if $\gcd(a,b)=1$ then $\gcd(a^2, b^2)=1$
37808
Show that $\gcd(a^2, b^2) = \gcd(a,b)^2$
31895
Prove that if $a$ and $b$ are odd, coprime numbers, then $\gcd(2^a +1, 2^b +1) = 3$
135086
GCD of two numbers divided by their greatest common divisor is 1
72747
Proving gcd($a,b$)lcm($a,b$) = $|ab|$
33996
Proving that $\gcd(2^m - 1, 2^n - 1) = 2^{\gcd(m,n )} - 1$
76680
Prove that if $\gcd(a,c)=1$ and $\gcd(b,c)=1$ then $\gcd(ab,c)=1$
4141
Prove: If $a\mid m$ and $b\mid m$ and $\gcd(a,b)=1$ then $ab\mid m$
82777
If $\gcd(a, b) = 1$ then prove that $\gcd(a+b, a^2-ab+b^2) = 1$ or $3$?
34059
$(a^{2^n}+1,a^{2^m}+1)=1 or 2$
21788
Proving that if $ad-bc = \pm 1$, then $\gcd(x,y) = \gcd(ax +by, cx + dy)$
19500
How can I find $\gcd(a^m+1,a^n+1)$ with $a,m,n$ positive integers?
152039
Prove that $a^{2^n}=1 \mod 2^{n+2}$