If $\gcd(a,x)=1$, then $a\mathbb N+b, x\mathbb N+y$ intersects.
14658
Deriving Chinese Remainder Theorem from gcd Bezout identity
37596
If $\gcd(a,b)= 1$ and $a$ divides $bc$ then $a$ divides $c\ $ [Euclid's Lemma]
107914
Expanding GCDs Reasoning: $\gcd(a,c) \cdot \gcd(b,c) = \gcd(ab,bc,ac,cc)$
21788
Proving that if $ad-bc = \pm 1$, then $\gcd(x,y) = \gcd(ax +by, cx + dy)$
105832
prove that if $\gcd(a,b)=1$ then $\gcd(a^2, b^2)=1$
113641
Suppose the gcd (a,b) = 1 and c divides a + b. Prove that gcd (a,c) = 1 = gcd (b,c)
147246
If $\gcd(a,c)=1=\gcd(b,c)$, then $\gcd(ab,c)=1$
84417
Prove that if $\gcd(a,b)=1$ then $\gcd(a^m, b)=1$
151434
If integers $a$ and $b$ are not both zero, then $\gcd(a,b)=\gcd(a-b,b)$
110313
Prove that $\gcd(f(x),g(x)) = 1$.
112486
Bounds on a sum of gcd's
158308
Proving that if $a,b$ are even, then $\gcd(a,b) = 2 \gcd(a/2, b/2)$
73391
Prove that if $\gcd(a,b)=1$, then $\gcd(a^2,b^2)=1$
59533
If $\gcd(m,n)=1$, then $\mathbb{Z}_n \times \mathbb{Z}_m$ is cyclic.
19656
Proving that $ \gcd(a,b) = as + bt $, i.e., $ \gcd $ is a linear combination.
90480
Code for (a,b) with gcd(a,b)=1?
19700
Prove that if $a$ and $b$ are relatively prime, then $\gcd(a+b, a-b) = 1$ or $2$