Let $a$ and $b$ be relatively prime integers. Find all possible values of $\gcd(a+2b,a-2b)$
25825
Proof that $\gcd(ax+by,cx+dy)=\gcd(x,y)$ if $ad-bc= \pm 1$
14783
A Number Theory problem (GCD)
35945
Proof that if $\gcd(a,b) = 1$ and $a\mid n$ and $b\mid n$, $ab \mid n$
77064
Proving $\gcd((a+b)^m,(a-b)^m)\le2^m$ for coprime $a,b$ and $m \in \Bbb N$
152878
calculate the gcd of $a+b$ and $p^4$
72672
Show that if $ar + bs = 1$ for some $r$ and $s$ then $a$ and $b$ are relatively prime
63965
How can I compute the sum of $ {m\over\gcd(m,n)}$?
3694
Show $GCD(a_1, a_2, a_3, \ldots , a_n)$ is the least positive integer that can be expressed in the form $a_1x_1+a_2x_2+ \ldots +a_nx_n$
51538
Intuition for $\,c\mid a,b \iff c\mid \gcd(a,b)$
135086
GCD of two numbers divided by their greatest common divisor is 1
83307
If $n\mid a^2-1$, $n$ an odd integer, show $n = \gcd(a-1, n)\gcd(a+1, n)$
62959
How to find GCD, LCM on a set of numbers
105444
Possible values of prime gaps
19656
Proving that $ \gcd(a,b) = as + bt $, i.e., $ \gcd $ is a linear combination.
48622
Given an integer $a$, suppose $d=\gcd(3a+5,\,5a+7)>2$. Determine $d$.
89066
Find all integers less than $m$ that are relatively prime to it
12862
Prove that two distinct numbers of the form $a^{2^{n}} + 1$ and $a^{2^{m}} + 1$ are relatively prime if $a$ is even and have $\gcd=2$ if $a$ is odd