Please find error in proof If c|a and c|b then $cgcd(a/c, b/c)=gcd(a, b)$
6410
Prove that $(ma, mb) = |m|(a, b)\ $ [GCD & LCM Distributive Law]
125737
GCD( LCM(a,b) , LCM(a,c) ) = LCM(b, GCD(b,c)) , why?
25825
Proof that $\gcd(ax+by,cx+dy)=\gcd(x,y)$ if $ad-bc= \pm 1$
114667
$d\mid a,b \iff d\mid\gcd(a,b) \ $ [GCD Universal Property]
76680
Prove that if $\gcd(a,c)=1$ and $\gcd(b,c)=1$ then $\gcd(ab,c)=1$
67660
Prove $\,b\equiv c\pmod{\!m}\Rightarrow \gcd(b,m)=\gcd(c,m)$ i.e. $\gcd(c+km,m) = \gcd(c,m)$
10348
Prove that if the $\gcd(a,b)=1$, then $\gcd(a+b,ab)=1$
110313
Prove that $\gcd(f(x),g(x)) = 1$.
126358
Prove for $\gcd$ of two integers $a,b$, that $(a^n,b^n) = (a,b)^n$
51538
Intuition for $\,c\mid a,b \iff c\mid \gcd(a,b)$
37808
Show that $\gcd(a^2, b^2) = \gcd(a,b)^2$
77064
Proving $\gcd((a+b)^m,(a-b)^m)\le2^m$ for coprime $a,b$ and $m \in \Bbb N$
19656
Proving that $ \gcd(a,b) = as + bt $, i.e., $ \gcd $ is a linear combination.
1713
number theory $\gcd(a,bc)=\gcd(a,c)$
130112
If $\gcd(a,n) = 1$ and $\gcd(b,n) = 1$, then $\gcd(ab,n) = 1$.
157508
prove $lcm(a,gcd(b,c))=gcd(lcm(a,b),lcm(a,c))$
147246
If $\gcd(a,c)=1=\gcd(b,c)$, then $\gcd(ab,c)=1$