Assuming that gcd(a,b)=1, show that gcd(a+b,a2-ab+b2)=1 or 3. Find an appropriate linear combination of a+b and a2-ab+b2. You may find the identity a2-ab+b2=(a+b)2-3ab helpful.

Which of the following options is correct?
A) gcd(a+b,a2-ab+b2)=1
B) gcd(a+b,a2-ab+b2)=3
C) gcd(a+b,a2-ab+b2)=1 or 3
D) gcd(a+b,a2-ab+b2)=2