GCD proof - by contradiction?
27250
Greatest common divisor of two relatively primes
1197
Finding $\gcd(2n-1,2n+1)$ . . . I think it's 1 but is my logic right?
91506
If $\gcd(a,b) = 1$ then $\gcd(a,a + b) = 1$
101872
Prove that $\gcd(a^2, b^2) = \gcd(a, b)^2$
33996
Proving that $\gcd(2^m - 1, 2^n - 1) = 2^{\gcd(m,n )} - 1$
19164
On the GCD of a Pair of Fermat Numbers
97469
How to prove $|a^k|=n/\gcd(n,k)$ whenever $|a|=n$?
87013
If $\gcd(a,b)=1$, then there exists integers $x$ and $y$ such that $xa + yb = 1$
130112
If $\gcd(a,n) = 1$ and $\gcd(b,n) = 1$, then $\gcd(ab,n) = 1$.
34738
Prove that $\gcd(n!+1,(n+1)!+1)=1$
28021
Showing that these two definitions of $\gcd(a,b)$ are equivalent
73391
Prove that if $\gcd(a,b)=1$, then $\gcd(a^2,b^2)=1$
1713
number theory $\gcd(a,bc)=\gcd(a,c)$
18772
If $a,b \in\mathbb N$ and $\gcd(a,b)=1$, prove that $\gcd(a+b;a^2+b^2)= 1$ or $2$.
95889
Prove that $\gcd(n! + 1, 3n! + 1) = 1$, $\forall n \in \mathbb{N}$, $n \geq 2$.
95533
I need some help with a GCD and LCM's Problem
136064
How can I prove that $\gcd(a,b)=1\implies \gcd(a^2,b^2)=1$ without using prime decomposition?