Question regarding $\gcd(a,b)=\gcd(b,r)$
190
Why $\gcd(qb+r,b)=\gcd(b,r)$?
130112
If $\gcd(a,n) = 1$ and $\gcd(b,n) = 1$, then $\gcd(ab,n) = 1$.
147802
Proving that $\gcd\left(\frac a {\gcd(a,b)},\frac b {\gcd(a,b)}\right) =1$
107914
Expanding GCDs Reasoning: $\gcd(a,c) \cdot \gcd(b,c) = \gcd(ab,bc,ac,cc)$
127993
Let $p$ be a prime. Suppose that $\gcd(a, b) = p$. Find $\gcd(a^2,b)$ for all integers $a$ and $b$.
63758
$c\mid ab\Rightarrow c\mid \gcd(a,c)\gcd(b,c),\,$ for integers $a, b, c$
113641
Suppose the gcd (a,b) = 1 and c divides a + b. Prove that gcd (a,c) = 1 = gcd (b,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
154959
Proof of associativity of GCD?
35945
Proof that if $\gcd(a,b) = 1$ and $a\mid n$ and $b\mid n$, $ab \mid n$
75974
$\gcd(a,b)\!=\!1\!=\!\gcd(a,c)\Rightarrow\gcd(a,bc)\!=\!1$ [coprimes to $\,a\,$ are product closed]
87846
If $\gcd (x,4) = 2$ and $\gcd(y,4) = 2$ then $\gcd(x+y,4) = 4$
4486
If $ar + bs =1$, then $\gcd(a,s) = \gcd(r,b) = \gcd(r,s) = 1$
10348
Prove that if the $\gcd(a,b)=1$, then $\gcd(a+b,ab)=1$
73391
Prove that if $\gcd(a,b)=1$, then $\gcd(a^2,b^2)=1$
147527
Let $a$ and $b$ be non-zero integers, and $c$ be an integer. Let $d = \gcd(a, b)$. Prove that if $a|c$ and $b|c$ then $ab|cd$.
105832
prove that if $\gcd(a,b)=1$ then $\gcd(a^2, b^2)=1$