If x2+y2x^2 + y^2x2+y2 is divisible by x+yx+yx+y, what is the relationship between gcd(x,y)\text{gcd}(x, y)gcd(x,y) and x+yx+yx+y?
gcd(x,y)=x+y\text{gcd}(x, y) = x+ygcd(x,y)=x+y
gcd(x,y)2\text{gcd}(x, y)^2gcd(x,y)2 divides x+yx+yx+y
gcd(x,y)=x+y2\text{gcd}(x, y) = \frac{x+y}{2}gcd(x,y)=2x+y
No specific relation