# Abstract algebra

• Jan 28th 2010, 04:26 PM
Deepu
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.
• Jan 28th 2010, 05:04 PM
Drexel28
Quote:

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.
• Jan 28th 2010, 05:08 PM
TheEmptySet
Quote:

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....
• Jan 30th 2010, 10:27 PM
Deepu
Quote:

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....