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Math Help - Abstract algebra

  1. #1
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    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.
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    MHF Contributor Drexel28's Avatar
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    Quote Originally Posted by Deepu View Post
    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.
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  3. #3
    Behold, the power of SARDINES!
    TheEmptySet's Avatar
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    Quote Originally Posted by Deepu View Post
    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....
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  4. #4
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    Quote Originally Posted by TheEmptySet View Post
    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....
    Can you please prove it..
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