Let d=gcd(a,b)d = \gcd(a, b)d=gcd(a,b). Which of the following statements about gcd(a+b,a−b)\gcd(a + b, a - b)gcd(a+b,a−b) must be true?
gcd(a+b,a−b)=d\gcd(a + b, a - b) = dgcd(a+b,a−b)=d
gcd(a+b,a−b)\gcd(a + b, a - b)gcd(a+b,a−b) divides 2d2d2d
gcd(a+b,a−b)=2d\gcd(a + b, a - b) = 2dgcd(a+b,a−b)=2d always
gcd(a+b,a−b)\gcd(a + b, a - b)gcd(a+b,a−b) is coprime to ddd