Simplifying $\gcd(a^x + 1, a^y + 1)$
66785
Find $\gcd(p^n-1,p^m+1)$.
69279
If $\gcd(a,b)=1$ then, $\gcd(a^2,b^2)=1$
80148
Prove $\gcd(a+b,a^2+b^2)$ is $1$ or $2$ if $\gcd(a,b) = 1$
13317
show that $a^{12} \equiv 1 \mod 32760$ for each $a \in \mathbb{Z}$ such that $\text{gcd}(a, 32760) = 1$
60596
Euclidean Algorithm for GCD of polynomials
69967
How to prove $\gcd(a^m-b^m,a^n-b^n) = a^{\gcd(m,n)} - b^{\gcd(m,n)} $?
147246
If $\gcd(a,c)=1=\gcd(b,c)$, then $\gcd(ab,c)=1$
28021
Showing that these two definitions of $\gcd(a,b)$ are equivalent
108450
Prove that $\gcd(a, b) = \gcd(a, b + ma)$?
33996
Proving that $\gcd(2^m - 1, 2^n - 1) = 2^{\gcd(m,n )} - 1$
92630
How to prove $\gcd(a^m,b^m) = \gcd(a,b)^m$ using Bézout's Lemma
25573
If $\gcd(a,b)=1$, then $\gcd(a+b,a^2 -ab+b^2)=1$ or $3$.
10966
gcd and lcm from prime factorization proof
2289
Prove that if $\gcd( a, b ) = 1$ then $\gcd( ac, b ) = \gcd( c, b ) $
77064
Proving $\gcd((a+b)^m,(a-b)^m)\le2^m$ for coprime $a,b$ and $m \in \Bbb N$
154959
Proof of associativity of GCD?
102133
Prove: $\gcd(a,b) = \gcd(a, b + at)$.