We denote by gcd (...) the greatest common divisor of the numbers in (...). (For example, gcd(4,6,8)=2 and gcd (12,15)=3.) Suppose that positive integers a,b,c satisfy the following four conditions:
∙ gcd (a,b,c)=1,
∙ gcd (a,b+c)>1,
∙ gcd (b,c+a)>1,
∙ gcd (c,a+b)>1.
a) Is it possible that a+b+c=2015?
b) Determine the minimum possible value that the sum a+b+c can take. number theorygreatest common divisormax