If $ar + bs =1$, then $\gcd(a,s) = \gcd(r,b) = \gcd(r,s) = 1$
72672
Show that if $ar + bs = 1$ for some $r$ and $s$ then $a$ and $b$ are relatively prime
28021
Showing that these two definitions of $\gcd(a,b)$ are equivalent
84417
Prove that if $\gcd(a,b)=1$ then $\gcd(a^m, b)=1$
21726
Show that if $(b,c)=1$, then $(a,bc)=(a,b)(a,c)$.
37808
Show that $\gcd(a^2, b^2) = \gcd(a,b)^2$
20878
If $(a,b)=1$ then prove $(a+b, ab)=1$.
66748
Show that if $a \equiv b \pmod n$, $\gcd(a,n)=\gcd(b,n)$
52546
How can I find the possible values that $\gcd(a+b,a^2+b^2)$ can take, if $\gcd(a,b)=1$
19700
Prove that if $a$ and $b$ are relatively prime, then $\gcd(a+b, a-b) = 1$ or $2$
130112
If $\gcd(a,n) = 1$ and $\gcd(b,n) = 1$, then $\gcd(ab,n) = 1$.
87013
If $\gcd(a,b)=1$, then there exists integers $x$ and $y$ such that $xa + yb = 1$
72747
Proving gcd($a,b$)lcm($a,b$) = $|ab|$
24160
Show that if $a$ is an odd integer and $b$ is an even integer then $\gcd(a,b)=\gcd(a,b/2)$
20823
If $\gcd(a,b) = 1$ and $a,b\mid x$ then $ab\mid x$.
147246
If $\gcd(a,c)=1=\gcd(b,c)$, then $\gcd(ab,c)=1$
101872
Prove that $\gcd(a^2, b^2) = \gcd(a, b)^2$
113641
Suppose the gcd (a,b) = 1 and c divides a + b. Prove that gcd (a,c) = 1 = gcd (b,c)