If $\gcd (a,b) = 1$, what can be said about $\gcd (a+b,a-b)$?
38404
Prove $\gcd(a+b, a-b) = 1$ or $2\,$ if $\,\gcd(a,b) = 1$
4486
If $ar + bs =1$, then $\gcd(a,s) = \gcd(r,b) = \gcd(r,s) = 1$
102133
Prove: $\gcd(a,b) = \gcd(a, b + at)$.
34330
How to prove $\gcd(a^2,b^2) = (\gcd(a,b))^2$?
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
2289
Prove that if $\gcd( a, b ) = 1$ then $\gcd( ac, b ) = \gcd( c, b ) $
158308
Proving that if $a,b$ are even, then $\gcd(a,b) = 2 \gcd(a/2, b/2)$
69279
If $\gcd(a,b)=1$ then, $\gcd(a^2,b^2)=1$
2208
$\gcd(a,b,c)=\gcd(\gcd(a,b),c)\,$ [GCD Associative Law]
37596
If $\gcd(a,b)= 1$ and $a$ divides $bc$ then $a$ divides $c\ $ [Euclid's Lemma]
422
If $\gcd(a,b)=1$, $\gcd(a,y)=1$ and $\gcd(b,x)=1$ then prove that $ax+by$ is prime to $ab$
11388
How you get from $\gcd(a,b)=1 \Longleftrightarrow ax+by=1 \Longrightarrow a \nmid b$?
128820
Prove that if $\gcd(a,b)=1$ then $\gcd(ab,c) = \gcd(a,c) \gcd(b,c)$
19656
Proving that $ \gcd(a,b) = as + bt $, i.e., $ \gcd $ is a linear combination.
7151
Let $a,m,n \in \mathbf{N}$. Show that if $\gcd(m,n)=1$, then $\gcd(a,mn)=\gcd(a,m)\cdot\gcd(a,n)$.
55673
Alternate proof that $\exists\ x \in \Bbb{Z}$ such that $ \gcd (a+bx,c) = 1$?
128199
Proving gcd(a, a+2) is 1 or 2 for every integer a?