Find $\gcd(a^{2^n}+1,a^{2^m}+1)$ where $m,n$ are two distinct positive integers.
19500
How can I find $\gcd(a^m+1,a^n+1)$ with $a,m,n$ positive integers?
103147
$\operatorname{gcd}(ab,a+b)=1$ if $a$ and $b$ are relatively prime
11388
How you get from $\gcd(a,b)=1 \Longleftrightarrow ax+by=1 \Longrightarrow a \nmid b$?
14783
A Number Theory problem (GCD)
18772
If $a,b \in\mathbb N$ and $\gcd(a,b)=1$, prove that $\gcd(a+b;a^2+b^2)= 1$ or $2$.
55441
Check: For the integers $a,b,c$ show that $\gcd(a,bc)=\gcd(a,\gcd(a,b)\cdot c)$
48622
Given an integer $a$, suppose $d=\gcd(3a+5,\,5a+7)>2$. Determine $d$.
33996
Proving that $\gcd(2^m - 1, 2^n - 1) = 2^{\gcd(m,n )} - 1$
1713
number theory $\gcd(a,bc)=\gcd(a,c)$
136064
How can I prove that $\gcd(a,b)=1\implies \gcd(a^2,b^2)=1$ without using prime decomposition?
37808
Show that $\gcd(a^2, b^2) = \gcd(a,b)^2$
102133
Prove: $\gcd(a,b) = \gcd(a, b + at)$.
79219
Prove that $a^{2^n} \equiv 1 \pmod{2^{n+2}},$ where $a$ is an odd integer.
86413
Show that $\frac{(m+n-1)!}{m!n!}$ is an integer where m and n are positive integers and gcd(m,n)=1
108450
Prove that $\gcd(a, b) = \gcd(a, b + ma)$?
122096
Find $GCD(n^2+1,n+1)$
82777
If $\gcd(a, b) = 1$ then prove that $\gcd(a+b, a^2-ab+b^2) = 1$ or $3$?