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Math Help - Generator

  1. #1
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    Generator

    Let p be a prime number. Then how many generators of the cyclic group Z_{p^r}, with r\in\mathbb{Z} and r\ge 1
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  2. #2
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    Quote Originally Posted by GTK X Hunter View Post
    Let p be a prime number. Then how many generators of the cyclic group Z_{p^r}, with r\in\mathbb{Z} and r\ge 1

    \mbox{An element}\,\,x\in Z_{p^r}\,\,\mbox{is a generator iff}\,\,(x,p^r)=1\,\,\mbox{, so there are....generators}

    Tonio
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  3. #3
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    Quote Originally Posted by tonio View Post
    \mbox{An element}\,\,x\in Z_{p^r}\,\,\mbox{is a generator iff}\,\,(x,p^r)=1\,\,\mbox{, so there are....generators}

    Tonio
    you mean the gcd (x,p^r)=1?
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