What is $\operatorname{gcd}(a,2^a-1)$?
33866
Show that $n$ does not divide $2^n - 1$ where $n$ is an integer greater than $1$?
19164
On the GCD of a Pair of Fermat Numbers
151520
About the parity of the product $(a_1-1)(a_2-2)\cdots(a_n-n)$
91506
If $\gcd(a,b) = 1$ then $\gcd(a,a + b) = 1$
56612
Proof of $\gcd(a,b)=ax+by\ $ [Bezout's identity]
51858
Showing $\gcd(2^m-1,2^n+1)=1$
63965
How can I compute the sum of $ {m\over\gcd(m,n)}$?
101872
Prove that $\gcd(a^2, b^2) = \gcd(a, b)^2$
11388
How you get from $\gcd(a,b)=1 \Longleftrightarrow ax+by=1 \Longrightarrow a \nmid b$?
57846
Multiplicative inverse in $\operatorname{GF}(2^8)$?
7091
If $\gcd(a,b)=1$, then $\gcd(a^n,b^n)=1$
23066
If $\gcd(a, b) = 1$, then $\gcd(ab, c) = \gcd(a, c) \cdot\gcd(b, c)$
74924
identity element of $(D_n ,\gcd)$
55441
Check: For the integers $a,b,c$ show that $\gcd(a,bc)=\gcd(a,\gcd(a,b)\cdot c)$
108450
Prove that $\gcd(a, b) = \gcd(a, b + ma)$?
69279
If $\gcd(a,b)=1$ then, $\gcd(a^2,b^2)=1$
11600
$\gcd(a,\operatorname{lcm}(b,c))=\operatorname{lcm}(\gcd(a,b),\gcd(a,c))$