# Abstract Algebra Proof (factorization?)

1. Feb 3, 2009

### dancergirlie

1. The problem statement, all variables and given/known data

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

2. Relevant 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

3. 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 =)