Prove that $\gcd(2^a - 1, 2^b - 1) = 2^{\gcd(a,b)} - 1$
33996
Proving that $\gcd(2^m - 1, 2^n - 1) = 2^{\gcd(m,n )} - 1$
126358
Prove for $\gcd$ of two integers $a,b$, that $(a^n,b^n) = (a,b)^n$
84501
Proof involving Cyclic group, generator and GCD
73391
Prove that if $\gcd(a,b)=1$, then $\gcd(a^2,b^2)=1$
2289
Prove that if $\gcd( a, b ) = 1$ then $\gcd( ac, b ) = \gcd( c, b ) $
7316
How to prove that $z\gcd(a,b)=\gcd(za,zb)$
110313
Prove that $\gcd(f(x),g(x)) = 1$.
53777
Why is $\gcd(x^4+1,x^2-1) = 1$ but I get $2$? [unit normalization of gcds]
85688
How to show $\gcd(ac, bd) = \gcd(a,d) * \gcd(b,c)$
95889
Prove that $\gcd(n! + 1, 3n! + 1) = 1$, $\forall n \in \mathbb{N}$, $n \geq 2$.
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 $a=b$
5789
$ d = \gcd(a,b)\Rightarrow\ \gcd(a/d,b/d) = 1$
108450
Prove that $\gcd(a, b) = \gcd(a, b + ma)$?
83307
If $n\mid a^2-1$, $n$ an odd integer, show $n = \gcd(a-1, n)\gcd(a+1, n)$
97469
How to prove $|a^k|=n/\gcd(n,k)$ whenever $|a|=n$?
100305
Prove $2^n-1$ is divisible by $(2^m-1)^2$ iff...
136304
Prove: $2^b-1\mid{}2^a-1 \iff b\mid{}a$