If d divides x and y, then it divides their x - y, so you cannot construct any other numbers. If x and y can be constructed, then can be constructed. It follows that gcd(x, y) can be constructed because it is calculated by Euclidean algorithm (which is just a series of modular divisions). So d can be constructed too. And finally, if max(x_i) = nd, then any number from the set kd = max(x_i) - (n - k)d = max(x_i) - d - d - ... can be constructed.