A man has three children. They are not triplets. By a remarkable coincidence, however, they were all born on the same day in different years. By another
remarkable coincidence, their ages right now form a Pythagorean triple. The
oldest child is nine years older than the youngest, and the middle child is two
years younger than the oldest.

a) How old are the three children?

b) The man knows that a multiple of a Pythagorean triple is also a Pythagorean triple. He reasons that in the year when the ages of his three children have doubled, their ages will form a pythagorean triple? Is he correct? Why or why not?