Prove that $\gcd(5x+2y,2x+y)=1$ if $\gcd(x,y)=1$
21788
Proving that if $ad-bc = \pm 1$, then $\gcd(x,y) = \gcd(ax +by, cx + dy)$
157508
prove $lcm(a,gcd(b,c))=gcd(lcm(a,b),lcm(a,c))$
60842
if $a^2+b^2=c^2$ then $gcd(a,b)=gcd(a,c)=gcd(b,c)$.
76507
$\gcd(b^x - 1, b^y - 1, b^ z- 1,\dots) = b^{\gcd(x, y, z,\dots)} -1$
19656
Proving that $ \gcd(a,b) = as + bt $, i.e., $ \gcd $ is a linear combination.
121156
Prove that: $\gcd[a,b,c]=\frac{abc.\operatorname{lcm}(a,b,c)}{\operatorname{lcm}(a,b)\operatorname{lcm}(a,c)\operatorname{lcm}(b,c)}$
66748
Show that if $a \equiv b \pmod n$, $\gcd(a,n)=\gcd(b,n)$
4486
If $ar + bs =1$, then $\gcd(a,s) = \gcd(r,b) = \gcd(r,s) = 1$
135086
GCD of two numbers divided by their greatest common divisor is 1
156641
Show that $\gcd(3n,3n+ 2) = 1$ when $n$ is odd
128199
Proving gcd(a, a+2) is 1 or 2 for every integer a?
139833
Prove that $\gcd(M, N)\times \mbox{lcm}(M, N) = M \times N$.
122096
Find $GCD(n^2+1,n+1)$
91506
If $\gcd(a,b) = 1$ then $\gcd(a,a + b) = 1$
19700
Prove that if $a$ and $b$ are relatively prime, then $\gcd(a+b, a-b) = 1$ or $2$
7091
If $\gcd(a,b)=1$, then $\gcd(a^n,b^n)=1$
87013
If $\gcd(a,b)=1$, then there exists integers $x$ and $y$ such that $xa + yb = 1$