prove that $\gcd(n^2+n ; n+2) = 1$ or $2$
73972
How to prove that $\gcd(2n^3-14n+2,n+3) = \gcd(n+3,10)$?
69279
If $\gcd(a,b)=1$ then, $\gcd(a^2,b^2)=1$
128820
Prove that if $\gcd(a,b)=1$ then $\gcd(ab,c) = \gcd(a,c) \gcd(b,c)$
38404
Prove $\gcd(a+b, a-b) = 1$ or $2\,$ if $\,\gcd(a,b) = 1$
34738
Prove that $\gcd(n!+1,(n+1)!+1)=1$
76680
Prove that if $\gcd(a,c)=1$ and $\gcd(b,c)=1$ then $\gcd(ab,c)=1$
34330
How to prove $\gcd(a^2,b^2) = (\gcd(a,b))^2$?
20003
Prove for positive integers a,b,c and d (where b does not equal d), if gcd(a,b) = gcd(c,d) = 1, then a/b + c/d is not an integer
84501
Proof involving Cyclic group, generator and GCD
2289
Prove that if $\gcd( a, b ) = 1$ then $\gcd( ac, b ) = \gcd( c, b ) $
59006
Proof of $\gcd(n!+1, (n+1)!+1)=1$?
66785
Find $\gcd(p^n-1,p^m+1)$.
28021
Showing that these two definitions of $\gcd(a,b)$ are equivalent
35945
Proof that if $\gcd(a,b) = 1$ and $a\mid n$ and $b\mid n$, $ab \mid n$
130112
If $\gcd(a,n) = 1$ and $\gcd(b,n) = 1$, then $\gcd(ab,n) = 1$.
82777
If $\gcd(a, b) = 1$ then prove that $\gcd(a+b, a^2-ab+b^2) = 1$ or $3$?
95889
Prove that $\gcd(n! + 1, 3n! + 1) = 1$, $\forall n \in \mathbb{N}$, $n \geq 2$.