Let $a,b,c$ be integers, no two of which are zero and $d=\gcd(a,b,c)$. Show that $d= \gcd(\gcd(a,b),c)$.
2208
$\gcd(a,b,c)=\gcd(\gcd(a,b),c)\,$ [GCD Associative Law]
76680
Prove that if $\gcd(a,c)=1$ and $\gcd(b,c)=1$ then $\gcd(ab,c)=1$
3694
Show $GCD(a_1, a_2, a_3, \ldots , a_n)$ is the least positive integer that can be expressed in the form $a_1x_1+a_2x_2+ \ldots +a_nx_n$
38404
Prove $\gcd(a+b, a-b) = 1$ or $2\,$ if $\,\gcd(a,b) = 1$
114667
$d\mid a,b \iff d\mid\gcd(a,b) \ $ [GCD Universal Property]
128199
Proving gcd(a, a+2) is 1 or 2 for every integer a?
67660
Prove $\,b\equiv c\pmod{\!m}\Rightarrow \gcd(b,m)=\gcd(c,m)$ i.e. $\gcd(c+km,m) = \gcd(c,m)$
69279
If $\gcd(a,b)=1$ then, $\gcd(a^2,b^2)=1$
84417
Prove that if $\gcd(a,b)=1$ then $\gcd(a^m, b)=1$
34738
Prove that $\gcd(n!+1,(n+1)!+1)=1$
1713
number theory $\gcd(a,bc)=\gcd(a,c)$
110313
Prove that $\gcd(f(x),g(x)) = 1$.
101872
Prove that $\gcd(a^2, b^2) = \gcd(a, b)^2$
34330
How to prove $\gcd(a^2,b^2) = (\gcd(a,b))^2$?
136064
How can I prove that $\gcd(a,b)=1\implies \gcd(a^2,b^2)=1$ without using prime decomposition?
27544
With $a,\ b,\ m,\ n\in \mathbb{Z}$. Show that if ${\rm gcd}(m,n)=1$, then ${\rm gcd}(ma+nb,mn)={\rm gcd}(a,n){\rm gcd}(b,m)$
126358
Prove for $\gcd$ of two integers $a,b$, that $(a^n,b^n) = (a,b)^n$