Prove that if $\operatorname{gcd}(a, b)=1$ then $\operatorname{gcd}(a c, b)=\operatorname{gcd}(c, b).$
55441
Check: For the integers $a,b,c$ show that $\gcd(a,bc)=\gcd(a,\gcd(a,b)\cdot c)$
157784
Prove that if $\gcd(ab,c)=1$, then $\gcd(a,c)=1$.
69279
If $\gcd(a,b)=1$ then, $\gcd(a^2,b^2)=1$
35945
Proof that if $\gcd(a,b) = 1$ and $a\mid n$ and $b\mid n$, $ab \mid n$
105832
prove that if $\gcd(a,b)=1$ then $\gcd(a^2, b^2)=1$
73391
Prove that if $\gcd(a,b)=1$, then $\gcd(a^2,b^2)=1$
72747
Proving gcd($a,b$)lcm($a,b$) = $|ab|$
56612
Proof of $\gcd(a,b)=ax+by\ $ [Bezout's identity]
85688
How to show $\gcd(ac, bd) = \gcd(a,d) * \gcd(b,c)$
4141
Prove: If $a\mid m$ and $b\mid m$ and $\gcd(a,b)=1$ then $ab\mid m$
157508
prove $lcm(a,gcd(b,c))=gcd(lcm(a,b),lcm(a,c))$
15168
If $a,b$ are positive integers such that $\gcd(a,b)=1$, then show that $\gcd(a+b, a-b)=1$ or $2$. and $\gcd(a^2+b^2, a^2-b^2)=1$ or $2 $
147802
Proving that $\gcd\left(\frac a {\gcd(a,b)},\frac b {\gcd(a,b)}\right) =1$
28021
Showing that these two definitions of $\gcd(a,b)$ are equivalent
102757
Prove that either $m$ divides $n$ or $n$ divides $m$ given that $\operatorname{lcm}(m,n) + \operatorname{gcd}(m,n) = m + n$?
18772
If $a,b \in\mathbb N$ and $\gcd(a,b)=1$, prove that $\gcd(a+b;a^2+b^2)= 1$ or $2$.
25713
If $a$ and $b$ commute and $\text{gcd}\left(\text{ord}(a),\text{ord}(b)\right)=1$, then $\text{ord}(ab)=\text{ord}(a)\text{ord}(b)$.