Let $a+b\mid ab$; extrapolates the $\gcd(a,b)$
63931
When $ab/(a+b)$ is an integer, where $a,b$ are positive integers.
147246
If $\gcd(a,c)=1=\gcd(b,c)$, then $\gcd(ab,c)=1$
154959
Proof of associativity of GCD?
83307
If $n\mid a^2-1$, $n$ an odd integer, show $n = \gcd(a-1, n)\gcd(a+1, n)$
20823
If $\gcd(a,b) = 1$ and $a,b\mid x$ then $ab\mid x$.
63758
$c\mid ab\Rightarrow c\mid \gcd(a,c)\gcd(b,c),\,$ for integers $a, b, c$
80148
Prove $\gcd(a+b,a^2+b^2)$ is $1$ or $2$ if $\gcd(a,b) = 1$
11388
How you get from $\gcd(a,b)=1 \Longleftrightarrow ax+by=1 \Longrightarrow a \nmid b$?
156966
Prove that if $b = dk$ where $gcd(m, a) = d$, there are $d$ solutions to $ax \equiv b \mod m$
114667
$d\mid a,b \iff d\mid\gcd(a,b) \ $ [GCD Universal Property]
35945
Proof that if $\gcd(a,b) = 1$ and $a\mid n$ and $b\mid n$, $ab \mid n$
135779
Prove the following: If $a \mid bc$, then $a \mid \gcd(a, b)c$.
19700
Prove that if $a$ and $b$ are relatively prime, then $\gcd(a+b, a-b) = 1$ or $2$
142693
$\gcd(a,b) = \gcd(a + b, \mathrm{lcm}[a,b])$
82777
If $\gcd(a, b) = 1$ then prove that $\gcd(a+b, a^2-ab+b^2) = 1$ or $3$?
157784
Prove that if $\gcd(ab,c)=1$, then $\gcd(a,c)=1$.
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 $