Prove that if $a$ and $b$ are relatively prime, then $\gcd(a+b, a-b) = 1$ or $2$
38404
Prove $\gcd(a+b, a-b) = 1$ or $2\,$ if $\,\gcd(a,b) = 1$
85688
How to show $\gcd(ac, bd) = \gcd(a,d) * \gcd(b,c)$
65687
$\gcd(a,b)\gcd(x,y)\mid ax+by$
10348
Prove that if the $\gcd(a,b)=1$, then $\gcd(a+b,ab)=1$
5789
$ d = \gcd(a,b)\Rightarrow\ \gcd(a/d,b/d) = 1$
76507
$\gcd(b^x - 1, b^y - 1, b^ z- 1,\dots) = b^{\gcd(x, y, z,\dots)} -1$
130653
$p^2$ divides $ab$ and $\gcd(a,b)=1$. Show $p^2$ divides $a$ or $p^2$ divides $b$
87846
If $\gcd (x,4) = 2$ and $\gcd(y,4) = 2$ then $\gcd(x+y,4) = 4$
113641
Suppose the gcd (a,b) = 1 and c divides a + b. Prove that gcd (a,c) = 1 = gcd (b,c)
422
If $\gcd(a,b)=1$, $\gcd(a,y)=1$ and $\gcd(b,x)=1$ then prove that $ax+by$ is prime to $ab$
72424
Suppose 1 ≤ k ≤ n − 1 and gcd(k, n) = 1. Prove that gcd(n − k, n) = 1
56612
Proof of $\gcd(a,b)=ax+by\ $ [Bezout's identity]
72672
Show that if $ar + bs = 1$ for some $r$ and $s$ then $a$ and $b$ are relatively prime
31895
Prove that if $a$ and $b$ are odd, coprime numbers, then $\gcd(2^a +1, 2^b +1) = 3$
101872
Prove that $\gcd(a^2, b^2) = \gcd(a, b)^2$
21788
Proving that if $ad-bc = \pm 1$, then $\gcd(x,y) = \gcd(ax +by, cx + dy)$
4486
If $ar + bs =1$, then $\gcd(a,s) = \gcd(r,b) = \gcd(r,s) = 1$