Show that $\gcd(a + b, a^2 + b^2) = 1$ or $2$ if $\gcd(a, b)=1$
52546
How can I find the possible values that $\gcd(a+b,a^2+b^2)$ can take, if $\gcd(a,b)=1$
7316
How to prove that $z\gcd(a,b)=\gcd(za,zb)$
20823
If $\gcd(a,b) = 1$ and $a,b\mid x$ then $ab\mid x$.
136064
How can I prove that $\gcd(a,b)=1\implies \gcd(a^2,b^2)=1$ without using prime decomposition?
127993
Let $p$ be a prime. Suppose that $\gcd(a, b) = p$. Find $\gcd(a^2,b)$ for all integers $a$ and $b$.
84417
Prove that if $\gcd(a,b)=1$ then $\gcd(a^m, b)=1$
1991
If $\gcd(a,b)=1$ and $a$ and $b$ divide $c$, then so does $ab$
87013
If $\gcd(a,b)=1$, then there exists integers $x$ and $y$ such that $xa + yb = 1$
90480
Code for (a,b) with gcd(a,b)=1?
10348
Prove that if the $\gcd(a,b)=1$, then $\gcd(a+b,ab)=1$
7091
If $\gcd(a,b)=1$, then $\gcd(a^n,b^n)=1$
20003
Prove for positive integers a,b,c and d (where b does not equal d), if gcd(a,b) = gcd(c,d) = 1, then a/b + c/d is not an integer
128820
Prove that if $\gcd(a,b)=1$ then $\gcd(ab,c) = \gcd(a,c) \gcd(b,c)$
156641
Show that $\gcd(3n,3n+ 2) = 1$ when $n$ is odd
72747
Proving gcd($a,b$)lcm($a,b$) = $|ab|$
102133
Prove: $\gcd(a,b) = \gcd(a, b + at)$.
101872
Prove that $\gcd(a^2, b^2) = \gcd(a, b)^2$