Show that if $\gcd(a,b)=1$ and $p$ is an odd prime, then
18714
$\gcd\left(a+b,\frac{a^p+b^p}{a+b}\right)=1$, or $p$
73391
Prove that if $\gcd(a,b)=1$, then $\gcd(a^2,b^2)=1$
57944
Euler's Formula application for distinct odd primes with gcd 1
25573
If $\gcd(a,b)=1$, then $\gcd(a+b,a^2 -ab+b^2)=1$ or $3$.
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 $a \mid \gcd(a, b)c$.
76680
Prove that if $\gcd(a,c)=1$ and $\gcd(b,c)=1$ then $\gcd(ab,c)=1$
147802
Proving that $\gcd\left(\frac a {\gcd(a,b)},\frac b {\gcd(a,b)}\right) =1$
69279
If $\gcd(a,b)=1$ then, $\gcd(a^2,b^2)=1$
37808
Show that $\gcd(a^2, b^2) = \gcd(a,b)^2$
140830
Show $\,p\mid 9^q -1 \implies q\mid p-1$ for odd primes $p$ and $q$
6012
Prove that $\gcd(a^n - 1, a^m - 1) = a^{\gcd(n, m)} - 1$
156641
Show that $\gcd(3n,3n+ 2) = 1$ when $n$ is odd
151434
If integers $a$ and $b$ are not both zero, then $\gcd(a,b)=\gcd(a-b,b)$
110313
Prove that $\gcd(f(x),g(x)) = 1$.
91506
If $\gcd(a,b) = 1$ then $\gcd(a,a + b) = 1$
38295
If $\gcd (a,b) = 1$, what can be said about $\gcd (a+b,a-b)$?