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Math Help - proof of this problem : if q|((b^m)-1) and (m|t) then q|((b^t)-1)

  1. #1
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    proof of this problem : if q|((b^m)-1) and (m|t) then q|((b^t)-1)

    hello.
    please help to proof this problem :

    if m is least number that q|((b^m)-1) and (m|t) then q|((b^t)-1).

    i don't know where to start.
    tanx
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  2. #2
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    Crna Gora
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    Re: proof of this problem : if q|((b^m)-1) and (m|t) then q|((b^t)-1)

    Use following Lemma :

    a^n-1=(a-1)\cdot \displaystyle \sum_{i=0}^{n-1} a^{i}

    b^t-1=b^{m\cdot k}-1=(b^{m})^{k}-1=(b^m-1)\cdot \displaystyle \sum_{i=0}^{k-1} b^{m\cdot i}
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