Use strong induction to show that every positive integer n can be written as a sum of distinct powers of two, that is, as a sum of a subset of the integers 20 = 1, 21 = 2, 22 = 4, and so on. Let P(n) be the proposition that the positive integer n can be written as a sum of distinct powers of 2. Identify the inductive hypothesis that proves P(n) is true. (You must provide an answer before moving to the next part.)