If gcd(a,b) = gcd(a,y) = gcd(b,x) = 1, then show that gcd(ax + by, ab) = 1.
422
If $\gcd(a,b)=1$, $\gcd(a,y)=1$ and $\gcd(b,x)=1$ then prove that $ax+by$ is prime to $ab$
105832
prove that if $\gcd(a,b)=1$ then $\gcd(a^2, b^2)=1$
91506
If $\gcd(a,b) = 1$ then $\gcd(a,a + b) = 1$
127993
Let $p$ be a prime. Suppose that $\gcd(a, b) = p$. Find $\gcd(a^2,b)$ for all integers $a$ and $b$.
128199
Proving gcd(a, a+2) is 1 or 2 for every integer a?
156966
Prove that if $b = dk$ where $gcd(m, a) = d$, there are $d$ solutions to $ax \equiv b \mod m$
2208
$\gcd(a,b,c)=\gcd(\gcd(a,b),c)\,$ [GCD Associative Law]
25907
Show $a\Bbb Z+b\Bbb Z = \gcd(a,b)\Bbb Z$
25825
Proof that $\gcd(ax+by,cx+dy)=\gcd(x,y)$ if $ad-bc= \pm 1$
65687
$\gcd(a,b)\gcd(x,y)\mid ax+by$
25573
If $\gcd(a,b)=1$, then $\gcd(a+b,a^2 -ab+b^2)=1$ or $3$.
37808
Show that $\gcd(a^2, b^2) = \gcd(a,b)^2$
11388
How you get from $\gcd(a,b)=1 \Longleftrightarrow ax+by=1 \Longrightarrow a \nmid b$?
69279
If $\gcd(a,b)=1$ then, $\gcd(a^2,b^2)=1$
107095
Prove $\gcd(a,b) \gcd(a,c) \gcd(b,c) \,\text{lcm} (a,b,c)^2=$ $\text{lcm}(a,b)\,\text{lcm}(a,c) \,\text{lcm}(b,c) \gcd(a,b,c)^2$
108450
Prove that $\gcd(a, b) = \gcd(a, b + ma)$?
59006
Proof of $\gcd(n!+1, (n+1)!+1)=1$?