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Number theorm - Euler theorem

  1. Feb 14, 2012 #1
    number theorm -- Euler theorem

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

    let be an integer that not divisible by 3. Prove that n^7[itex]\equiv[/itex]n mod 63

    2. Relevant equations


    3. The attempt at a solution
    it is suffice to prove that n^7[itex]\equiv[/itex]n mod 7,n^7[itex]\equiv[/itex]n mod 9, i get
    n^7[itex]\equiv[/itex]n mod 7 by Euler theorem , how to prove n^7[itex]\equiv[/itex]n mod 9
  2. jcsd
  3. Feb 14, 2012 #2
    Re: number theorm -- Euler theorem

    Remember that Euler's totient function, [itex]\varphi (n)[/itex] is equal to the number of positive integers less than or equal to n that are coprime to n. What is [itex]\varphi (9)[/itex] and what does that imply by Euler's Theorem?
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