Show that $\gcd(a + b, a^2 + b^2) = 1\mbox{ or } 2$
52546
How can I find the possible values that $\gcd(a+b,a^2+b^2)$ can take, if $\gcd(a,b)=1$
122096
Find $GCD(n^2+1,n+1)$
87846
If $\gcd (x,4) = 2$ and $\gcd(y,4) = 2$ then $\gcd(x+y,4) = 4$
20823
If $\gcd(a,b) = 1$ and $a,b\mid x$ then $ab\mid x$.
128199
Proving gcd(a, a+2) is 1 or 2 for every integer a?
25573
If $\gcd(a,b)=1$, then $\gcd(a+b,a^2 -ab+b^2)=1$ or $3$.
59006
Proof of $\gcd(n!+1, (n+1)!+1)=1$?
128820
Prove that if $\gcd(a,b)=1$ then $\gcd(ab,c) = \gcd(a,c) \gcd(b,c)$
84417
Prove that if $\gcd(a,b)=1$ then $\gcd(a^m, b)=1$
156641
Show that $\gcd(3n,3n+ 2) = 1$ when $n$ is odd
6012
Prove that $\gcd(a^n - 1, a^m - 1) = a^{\gcd(n, m)} - 1$
19700
Prove that if $a$ and $b$ are relatively prime, then $\gcd(a+b, a-b) = 1$ or $2$
24160
Show that if $a$ is an odd integer and $b$ is an even integer then $\gcd(a,b)=\gcd(a,b/2)$
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 $
83307
If $n\mid a^2-1$, $n$ an odd integer, show $n = \gcd(a-1, n)\gcd(a+1, n)$
56612
Proof of $\gcd(a,b)=ax+by\ $ [Bezout's identity]
34738
Prove that $\gcd(n!+1,(n+1)!+1)=1$