Prove that the gcd of ( 8n+19 , 3n+7 ) =1
25825
Proof that $\gcd(ax+by,cx+dy)=\gcd(x,y)$ if $ad-bc= \pm 1$
5708
Prove that if $k\ge 1\,$ and $\,a^k\equiv 1\pmod{\! n}$ then $\gcd(a,n)=1$
76507
$\gcd(b^x - 1, b^y - 1, b^ z- 1,\dots) = b^{\gcd(x, y, z,\dots)} -1$
63758
$c\mid ab\Rightarrow c\mid \gcd(a,c)\gcd(b,c),\,$ for integers $a, b, c$
37808
Show that $\gcd(a^2, b^2) = \gcd(a,b)^2$
147802
Proving that $\gcd\left(\frac a {\gcd(a,b)},\frac b {\gcd(a,b)}\right) =1$
99428
Prove that $3^{2n-1} + 2^{n+1}$ is always a multiple of $7$.
105832
prove that if $\gcd(a,b)=1$ then $\gcd(a^2, b^2)=1$
36
Prove: If $\gcd(a,b,c)=1$ then there exists $z$ such that $\gcd(az+b,c) = 1$
69279
If $\gcd(a,b)=1$ then, $\gcd(a^2,b^2)=1$
66016
Prove $3^{2n+1} + 2^{n+2}$ is divisible by $7$ for all $n\ge0$
66785
Find $\gcd(p^n-1,p^m+1)$.
24845
Let $a\mid c$ and $b\mid c$ such that $\gcd(a,b)=1$, Show that $ab\mid c$
20574
Understanding the proof for $\gcd (F_n, F_{n+k}) = 1$ where $F_n$ is a Fermat number
127833
Proving that $7^n(3n+1)-1$ is divisible by 9
135779
Prove the following: If $a \mid bc$, then $a \mid \gcd(a, b)c$.
25573
If $\gcd(a,b)=1$, then $\gcd(a+b,a^2 -ab+b^2)=1$ or $3$.