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 2^0 = 1.2^1 = 2. 2^2 =4. and so on. (hint: for the inductive step, separately con- sider the case where k + 1 is even and where it is odd. when it is even, note that (k + 1)/2 is an integer.]