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Math Help - Cyclic groups.

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    MHF Contributor Also sprach Zarathustra's Avatar
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    Cyclic groups.

    Let G be a cyclic groups. (Exist x\in G so that G=<x>={x^n:n\in \mathbb{Z})

    Show that if ord(x)=n then the number of genereted elements of <x> is \phi(n).
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    Quote Originally Posted by Also sprach Zarathustra View Post
    Let G be a cyclic groups. (Exist x\in G so that G=<x>={x^n:n\in \mathbb{Z})

    Show that if ord(x)=n then the number of genereted elements of <x> is \phi(n).

    Hint: show that x^k is a generator of the group iff gcd(k,n)=1 , using Euclides algorithm.

    Tonio
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