Given that $gcd(a,b)=1$, prove that $gcd(a+b,a^2-ab+b^2)=1$ or $3$, also when will it equal $1$?
25573
If $\gcd(a,b)=1$, then $\gcd(a+b,a^2 -ab+b^2)=1$ or $3$.
113641
Suppose the gcd (a,b) = 1 and c divides a + b. Prove that gcd (a,c) = 1 = gcd (b,c)
156641
Show that $\gcd(3n,3n+ 2) = 1$ when $n$ is odd
128820
Prove that if $\gcd(a,b)=1$ then $\gcd(ab,c) = \gcd(a,c) \gcd(b,c)$
103147
$\operatorname{gcd}(ab,a+b)=1$ if $a$ and $b$ are relatively prime
7090
Show that $\gcd(a,bc)=1$ if and only if $\gcd(a,b)=1$ and $\gcd(a,c)=1$
73391
Prove that if $\gcd(a,b)=1$, then $\gcd(a^2,b^2)=1$
135779
Prove the following: If $a \mid bc$, then $a \mid \gcd(a, b)c$.
91506
If $\gcd(a,b) = 1$ then $\gcd(a,a + b) = 1$
127993
Let $p$ be a prime. Suppose that $\gcd(a, b) = p$. Find $\gcd(a^2,b)$ for all integers $a$ and $b$.
92645
Why isn't $\gcd(x^2+3x+2,x^2+x)=(x+1)$? [unit normalization of gcds]
23066
If $\gcd(a, b) = 1$, then $\gcd(ab, c) = \gcd(a, c) \cdot\gcd(b, c)$
31895
Prove that if $a$ and $b$ are odd, coprime numbers, then $\gcd(2^a +1, 2^b +1) = 3$
1713
number theory $\gcd(a,bc)=\gcd(a,c)$
38404
Prove $\gcd(a+b, a-b) = 1$ or $2\,$ if $\,\gcd(a,b) = 1$
49109
Proving $\gcd \left(\frac{a}{\gcd (a,b)},\frac{b}{\gcd (a,b)}\right)=1$
7091
If $\gcd(a,b)=1$, then $\gcd(a^n,b^n)=1$