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Math Help - Using the chinese remainder theorem to prove a bijection

  1. #1
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    Using the chinese remainder theorem to prove a bijection

    I have a problem where I have to prove that \phi(nm)=\phi(m)\phi(n) where n and m are relatively prime and \phi is Euler's totent.

    I know that for the proof I must show that there is a bijection between mn and m \times n and I am having troubles doing that. Any help would be appreciated.
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  2. #2
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    Quote Originally Posted by chiefbutz View Post
    I have a problem where I have to prove that \phi(nm)=\phi(m)\phi(n) where n and m are relatively prime and \phi is Euler's totent.

    I know that for the proof I must show that there is a bijection between mn and m \times n and I am having troubles doing that. Any help would be appreciated.

    Bijection between mn\,\,\,and\,\,\,m\times n?? How? What are these things? You may, or may not, have a bijection between sets: what are the sets here?

    Tonio
    Last edited by tonio; February 7th 2010 at 11:53 AM.
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  3. #3
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    Quote Originally Posted by tonio View Post
    What are these things?
    Oops, sorry. I forgot to include that m and n are both Natural numbers.
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  4. #4
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    Can't anyone help? Please?
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  5. #5
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    Quote Originally Posted by chiefbutz View Post
    Oops, sorry. I forgot to include that m and n are both Natural numbers.

    You still haven't answered my question: if m,n are natural numbers then mn is again a natural number and, I suppose, m\times n may be, again, a natural numer. You can, of course, define a very boring correspondence between the two sets containing each one of these numbers ( that'd be exactly the same set if both mn\,,\,\,m\times n happen to be the very same natural number) so again I ask: what correspondence, between WHICH SETS, are you talking about??

    Mathematics is not just trying to solve problems: one must also strive to understand what one's talking about, the symbols and etc.

    Tonio
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