Prove that $\gcd(3^n-2,2^n-3)=1$ if and only if $\gcd(6^n-4,2^n-3)=1$
20477
Prove that $\gcd(3^n-2,2^n-3)=\gcd(5,2^n-3)$
1713
number theory $\gcd(a,bc)=\gcd(a,c)$
122096
Find $GCD(n^2+1,n+1)$
55441
Check: For the integers $a,b,c$ show that $\gcd(a,bc)=\gcd(a,\gcd(a,b)\cdot c)$
25573
If $\gcd(a,b)=1$, then $\gcd(a+b,a^2 -ab+b^2)=1$ or $3$.
20574
Understanding the proof for $\gcd (F_n, F_{n+k}) = 1$ where $F_n$ is a Fermat number
38404
Prove $\gcd(a+b, a-b) = 1$ or $2\,$ if $\,\gcd(a,b) = 1$
95061
Proving that $2^{2\cdot 3^{n-1}}\equiv 1+3^n\pmod{3^{n+1}}$ for every natural $n$
85688
How to show $\gcd(ac, bd) = \gcd(a,d) * \gcd(b,c)$
4141
Prove: If $a\mid m$ and $b\mid m$ and $\gcd(a,b)=1$ then $ab\mid m$
158308
Proving that if $a,b$ are even, then $\gcd(a,b) = 2 \gcd(a/2, b/2)$
22845
Prove that if d is a common divisor of a and b, then $d=\gcd(a,b)$ if and only if $\gcd(a/d,b/d)=1$
18772
If $a,b \in\mathbb N$ and $\gcd(a,b)=1$, prove that $\gcd(a+b;a^2+b^2)= 1$ or $2$.
82777
If $\gcd(a, b) = 1$ then prove that $\gcd(a+b, a^2-ab+b^2) = 1$ or $3$?
92630
How to prove $\gcd(a^m,b^m) = \gcd(a,b)^m$ using Bézout's Lemma
31895
Prove that if $a$ and $b$ are odd, coprime numbers, then $\gcd(2^a +1, 2^b +1) = 3$
76680
Prove that if $\gcd(a,c)=1$ and $\gcd(b,c)=1$ then $\gcd(ab,c)=1$