Prove GCD statement with multiple variables
3694
Show $GCD(a_1, a_2, a_3, \ldots , a_n)$ is the least positive integer that can be expressed in the form $a_1x_1+a_2x_2+ \ldots +a_nx_n$
31465
Prove that if $a \mid b$ then $\gcd(a,b) = |a|$
51858
Showing $\gcd(2^m-1,2^n+1)=1$
38404
Prove $\gcd(a+b, a-b) = 1$ or $2\,$ if $\,\gcd(a,b) = 1$
1713
number theory $\gcd(a,bc)=\gcd(a,c)$
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
44076
Proving if $d_0$ is the smallest positive integer in $S$ then $d_0 = \gcd(a,b)$
147802
Proving that $\gcd\left(\frac a {\gcd(a,b)},\frac b {\gcd(a,b)}\right) =1$
122096
Find $GCD(n^2+1,n+1)$
28021
Showing that these two definitions of $\gcd(a,b)$ are equivalent
87013
If $\gcd(a,b)=1$, then there exists integers $x$ and $y$ such that $xa + yb = 1$
101872
Prove that $\gcd(a^2, b^2) = \gcd(a, b)^2$
4141
Prove: If $a\mid m$ and $b\mid m$ and $\gcd(a,b)=1$ then $ab\mid m$
25907
Show $a\Bbb Z+b\Bbb Z = \gcd(a,b)\Bbb Z$
76507
$\gcd(b^x - 1, b^y - 1, b^ z- 1,\dots) = b^{\gcd(x, y, z,\dots)} -1$
66748
Show that if $a \equiv b \pmod n$, $\gcd(a,n)=\gcd(b,n)$
14783
A Number Theory problem (GCD)