If $\gcd(n,a)=1$, and $\gcd(n,b)=1$ prove $\gcd(n,ab)=1$
130112
If $\gcd(a,n) = 1$ and $\gcd(b,n) = 1$, then $\gcd(ab,n) = 1$.
126358
Prove for $\gcd$ of two integers $a,b$, that $(a^n,b^n) = (a,b)^n$
147246
If $\gcd(a,c)=1=\gcd(b,c)$, then $\gcd(ab,c)=1$
55441
Check: For the integers $a,b,c$ show that $\gcd(a,bc)=\gcd(a,\gcd(a,b)\cdot c)$
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 $ab|cd$.
90480
Code for (a,b) with gcd(a,b)=1?
69967
How to prove $\gcd(a^m-b^m,a^n-b^n) = a^{\gcd(m,n)} - b^{\gcd(m,n)} $?
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
103147
$\operatorname{gcd}(ab,a+b)=1$ if $a$ and $b$ are relatively prime
149993
Use the Euclidean algorithm to prove that gcd(na, nb) = n gcd(a, b).
1713
number theory $\gcd(a,bc)=\gcd(a,c)$
34330
How to prove $\gcd(a^2,b^2) = (\gcd(a,b))^2$?
66748
Show that if $a \equiv b \pmod n$, $\gcd(a,n)=\gcd(b,n)$
112031
Prove that $\gcd(2^{2^m}+1,2^{2^n}+1)=1$ if $m,n$ are positive integers.
158308
Proving that if $a,b$ are even, then $\gcd(a,b) = 2 \gcd(a/2, b/2)$
151434
If integers $a$ and $b$ are not both zero, then $\gcd(a,b)=\gcd(a-b,b)$
91506
If $\gcd(a,b) = 1$ then $\gcd(a,a + b) = 1$