Question

If a and b are co-prime then prove that gcd(a+b, a²-ab +b²) = 1 or 3.​

Answer 1

Answer:

Hint: a2−ab+b2=(a+b)2−3ab.a2−ab+b2=(a+b)2−3ab.

I know we can say that there exists an x,yx,y such that ax+by=1ax+by=1. So in this case, (a+b)x+((a+b)2−3ab)y=1.(a+b)x+((a+b)2−3ab)y=1.

I thought setting x=(a+b)x=(a+b) and y=−1y=−1 would help but that gives me 3ab=1

Mark me as brainlist