How do you show gcd( p+qi, p-qi) | 2 in this case?
38295
If $\gcd (a,b) = 1$, what can be said about $\gcd (a+b,a-b)$?
25573
If $\gcd(a,b)=1$, then $\gcd(a+b,a^2 -ab+b^2)=1$ or $3$.
60596
Euclidean Algorithm for GCD of polynomials
28021
Showing that these two definitions of $\gcd(a,b)$ are equivalent
92630
How to prove $\gcd(a^m,b^m) = \gcd(a,b)^m$ using Bézout's Lemma
91506
If $\gcd(a,b) = 1$ then $\gcd(a,a + b) = 1$
85449
Show a,b,c congruences when $a^2+b^2=c^2$
82777
If $\gcd(a, b) = 1$ then prove that $\gcd(a+b, a^2-ab+b^2) = 1$ or $3$?
156641
Show that $\gcd(3n,3n+ 2) = 1$ when $n$ is odd
55441
Check: For the integers $a,b,c$ show that $\gcd(a,bc)=\gcd(a,\gcd(a,b)\cdot c)$
19500
How can I find $\gcd(a^m+1,a^n+1)$ with $a,m,n$ positive integers?
80148
Prove $\gcd(a+b,a^2+b^2)$ is $1$ or $2$ if $\gcd(a,b) = 1$
83307
If $n\mid a^2-1$, $n$ an odd integer, show $n = \gcd(a-1, n)\gcd(a+1, n)$
66748
Show that if $a \equiv b \pmod n$, $\gcd(a,n)=\gcd(b,n)$
190
Why $\gcd(qb+r,b)=\gcd(b,r)$?
48839
Show that the order of $a\times b$ is equal to $nm$ if gcd(n,m)=1
147307
How to evaluate $\sum_{\gcd (p,q)=1} \frac{1}{p^2q^2}$?