Prove that if $\gcd(a,b)=1$ then $\gcd(a,bc) = \gcd(a,c)$.
55441
Check: For the integers $a,b,c$ show that $\gcd(a,bc)=\gcd(a,\gcd(a,b)\cdot c)$
21726
Show that if $(b,c)=1$, then $(a,bc)=(a,b)(a,c)$.
85688
How to show $\gcd(ac, bd) = \gcd(a,d) * \gcd(b,c)$
7151
Let $a,m,n \in \mathbf{N}$. Show that if $\gcd(m,n)=1$, then $\gcd(a,mn)=\gcd(a,m)\cdot\gcd(a,n)$.
112031
Prove that $\gcd(2^{2^m}+1,2^{2^n}+1)=1$ if $m,n$ are positive integers.
84417
Prove that if $\gcd(a,b)=1$ then $\gcd(a^m, b)=1$
87013
If $\gcd(a,b)=1$, then there exists integers $x$ and $y$ such that $xa + yb = 1$
136064
How can I prove that $\gcd(a,b)=1\implies \gcd(a^2,b^2)=1$ without using prime decomposition?
147246
If $\gcd(a,c)=1=\gcd(b,c)$, then $\gcd(ab,c)=1$
108450
Prove that $\gcd(a, b) = \gcd(a, b + ma)$?
135779
Prove the following: If $a \mid bc$, then $a \mid \gcd(a, b)c$.
102133
Prove: $\gcd(a,b) = \gcd(a, b + at)$.
77278
If $\,\gcd(a,b) = {\rm lcm}(a,b)\,$ then prove $a=b$
113641
Suppose the gcd (a,b) = 1 and c divides a + b. Prove that gcd (a,c) = 1 = gcd (b,c)
31331
$|a|=m,\,\gcd(m,n)=1 \implies a$ is an $n$'th power
2208
$\gcd(a,b,c)=\gcd(\gcd(a,b),c)\,$ [GCD Associative Law]
49109
Proving $\gcd \left(\frac{a}{\gcd (a,b)},\frac{b}{\gcd (a,b)}\right)=1$