prove that if gcd(a,b) = 1, then gcd(a,a+b) = 1
91506
If $\gcd(a,b) = 1$ then $\gcd(a,a + b) = 1$
80148
Prove $\gcd(a+b,a^2+b^2)$ is $1$ or $2$ if $\gcd(a,b) = 1$
7151
Let $a,m,n \in \mathbf{N}$. Show that if $\gcd(m,n)=1$, then $\gcd(a,mn)=\gcd(a,m)\cdot\gcd(a,n)$.
19656
Proving that $ \gcd(a,b) = as + bt $, i.e., $ \gcd $ is a linear combination.
72747
Proving gcd($a,b$)lcm($a,b$) = $|ab|$
20823
If $\gcd(a,b) = 1$ and $a,b\mid x$ then $ab\mid x$.
112031
Prove that $\gcd(2^{2^m}+1,2^{2^n}+1)=1$ if $m,n$ are positive integers.
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 $
38295
If $\gcd (a,b) = 1$, what can be said about $\gcd (a+b,a-b)$?
87013
If $\gcd(a,b)=1$, then there exists integers $x$ and $y$ such that $xa + yb = 1$
2289
Prove that if $\gcd( a, b ) = 1$ then $\gcd( ac, b ) = \gcd( c, b ) $
105832
prove that if $\gcd(a,b)=1$ then $\gcd(a^2, b^2)=1$
6012
Prove that $\gcd(a^n - 1, a^m - 1) = a^{\gcd(n, m)} - 1$
157784
Prove that if $\gcd(ab,c)=1$, then $\gcd(a,c)=1$.
157508
prove $lcm(a,gcd(b,c))=gcd(lcm(a,b),lcm(a,c))$
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 $\gcd(a,n)=1$