If $gcd(a,b)=1$ then $gcd\big(\frac{a^{p}+b^{p}}{a+b},a+b\big)=1$ unless $p|a+b$
23590
Show that $\gcd\left(\frac{a^n-b^n}{a-b},a-b\right)=\gcd(n d^{n-1},a-b)$
87013
If $\gcd(a,b)=1$, then there exists integers $x$ and $y$ such that $xa + yb = 1$
77278
If $\,\gcd(a,b) = {\rm lcm}(a,b)\,$ then prove $a=b$
59006
Proof of $\gcd(n!+1, (n+1)!+1)=1$?
422
If $\gcd(a,b)=1$, $\gcd(a,y)=1$ and $\gcd(b,x)=1$ then prove that $ax+by$ is prime to $ab$
76507
$\gcd(b^x - 1, b^y - 1, b^ z- 1,\dots) = b^{\gcd(x, y, z,\dots)} -1$
2208
$\gcd(a,b,c)=\gcd(\gcd(a,b),c)\,$ [GCD Associative Law]
31465
Prove that if $a \mid b$ then $\gcd(a,b) = |a|$
80148
Prove $\gcd(a+b,a^2+b^2)$ is $1$ or $2$ if $\gcd(a,b) = 1$
4141
Prove: If $a\mid m$ and $b\mid m$ and $\gcd(a,b)=1$ then $ab\mid m$
85688
How to show $\gcd(ac, bd) = \gcd(a,d) * \gcd(b,c)$
19500
How can I find $\gcd(a^m+1,a^n+1)$ with $a,m,n$ positive integers?
136064
How can I prove that $\gcd(a,b)=1\implies \gcd(a^2,b^2)=1$ without using prime decomposition?
147527
Let $a$ and $b$ be non-zero integers, and $c$ be an integer. Let $d = \gcd(a, b)$. Prove that if $a|c$ and $b|c$ then $ab|cd$.
49109
Proving $\gcd \left(\frac{a}{\gcd (a,b)},\frac{b}{\gcd (a,b)}\right)=1$
84417
Prove that if $\gcd(a,b)=1$ then $\gcd(a^m, b)=1$
105832
prove that if $\gcd(a,b)=1$ then $\gcd(a^2, b^2)=1$