GCD (a,b) =1 prove GCD ( (a+b), (a-b) ) = 1 or 2
38404
Prove $\gcd(a+b, a-b) = 1$ or $2\,$ if $\,\gcd(a,b) = 1$
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 $ab|cd$.
73391
Prove that if $\gcd(a,b)=1$, then $\gcd(a^2,b^2)=1$
76507
$\gcd(b^x - 1, b^y - 1, b^ z- 1,\dots) = b^{\gcd(x, y, z,\dots)} -1$
87846
If $\gcd (x,4) = 2$ and $\gcd(y,4) = 2$ then $\gcd(x+y,4) = 4$
18772
If $a,b \in\mathbb N$ and $\gcd(a,b)=1$, prove that $\gcd(a+b;a^2+b^2)= 1$ or $2$.
25907
Show $a\Bbb Z+b\Bbb Z = \gcd(a,b)\Bbb Z$
7091
If $\gcd(a,b)=1$, then $\gcd(a^n,b^n)=1$
49109
Proving $\gcd \left(\frac{a}{\gcd (a,b)},\frac{b}{\gcd (a,b)}\right)=1$
22845
Prove that if d is a common divisor of a and b, then $d=\gcd(a,b)$ if and only if $\gcd(a/d,b/d)=1$
5708
Prove that if $k\ge 1\,$ and $\,a^k\equiv 1\pmod{\! n}$ then $\gcd(a,n)=1$
87013
If $\gcd(a,b)=1$, then there exists integers $x$ and $y$ such that $xa + yb = 1$
15168
If $a,b$ are positive integers such that $\gcd(a,b)=1$, then show that $\gcd(a+b, a-b)=1$ or $2$. and $\gcd(a^2+b^2, a^2-b^2)=1$ or $2 $
91506
If $\gcd(a,b) = 1$ then $\gcd(a,a + b) = 1$
38295
If $\gcd (a,b) = 1$, what can be said about $\gcd (a+b,a-b)$?
117098
Properties of the greatest common divisor: $\gcd(a, b) = \gcd(a, b-a)$ and $\gcd(a, b) = \gcd(a, b \text{ mod } a)$
4486
If $ar + bs =1$, then $\gcd(a,s) = \gcd(r,b) = \gcd(r,s) = 1$