- #1

dancergirlie

- 200

- 0

## Homework Statement

If n is a nonzero integer, prove that n cam be written uniquely in the form n=(2^k)m, where k is greater than or equal to zero, and m is odd

## Homework Equations

It is in the primes and unique factorization chapter so maybe that every integer n (except 0 and 1) can be written as a product of primes

## The Attempt at a Solution

I am not sure, but I tried to do a proof by induction on n

Let n=1

so, 1=(2^k)(m)

1=(1)(1)=1 where k=0 and m=1

so the statement holds for n=1

Now assume the statement holds for n=(r-1) for any integer (except 0 and 1)

so

(r-1)=(2^k)(m) where k is greater than or equal to zero and m is odd

Now let n=r

so r=(2^k)(m)

This is where I don't know what to do... that is why I'm thinking there is an easier way to do this besides induction. Any help would be appreciated =)