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 ,261=2, 2^2=4,... [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+2)/2 is an integer.]