Use strong induction to show that every positive integer n canbe written as a sum of distinct powers of two, that is, as a sum ofa subset of the integers 2^0 =1, 2^1 = 2, 2^2 = 4, and so on.[Hint: For the inductive step, separately consider the case where k+ 1 is even and where it is odd. When it is even, note that (k +1)/2 is an integer.]
