If we consider an odd number your are right...
I think its true that for every positive natural number, lets call it n, can be put in form of 2^k * m (where m is an odd number).
I think thats correct? Please confirm...
How would you use direct proof to proof this?? I cant get grips of it. Its abit advanced for me
if n is odd choose k = 0 and m = n.
if n is even then write in its prime decomposition.
Choose k=r and choose to be the product of primes, . The product of primes is guaranteed to be odd because an odd times an odd is an odd and no primes other than 2 are even. If there are no s (ie. n is a power of 2), then take m=1.