1. Abstract algebra

if n belongs to integer and n is not equal to 0, prove that n can be written uniquely in the form n=2^k * m, where k>=0 and m is odd.

2. Originally Posted by Deepu
if n belongs to integer and n is not equal to 0, prove that n can be written uniquely in the form n=2^k * m, where k>=0 and m is odd.
What have you tried???

P.S. WHY do you keep labeling these abstract algebra???? I get all excited to answer a question on free groups or something and when I get here....number theory . Juts becuase you are doing something in an abstract algebra course does it mean it is abstract algebra.

3. Originally Posted by Deepu
if n belongs to integer and n is not equal to 0, prove that n can be written uniquely in the form n=2^k * m, where k>=0 and m is odd.
Here are some hints:

First note every natual number has a unique factorization.

Second note 2 is the only even prime number.

3rd the product of two odd numbers is....

4. Originally Posted by TheEmptySet
Here are some hints:

First note every natual number has a unique factorization.

Second note 2 is the only even prime number.

3rd the product of two odd numbers is....