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Math Help - arithmetic in Z/nZ

  1. #1
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    arithmetic in Z/nZ

    Any help greatly appreciated!!

    I can do similar ones such as x^6 - 14 = 0 in Z/65Z, but this one with 4 to the power of x, has me stuck.


    Solve the following equation:

    4^x +2 = 0 in Z/29Z,
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  2. #2
    MHF Contributor

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    Quote Originally Posted by rmangan View Post

    Solve the following equation: 4^x +2 \equiv 0 \mod 29.
    the equation has no solution: first note that: 4^x=(2^x)^2. now we have \frac{29 - 1}{2}=14 and \frac{29^2 - 1}{8}=105. therefore: \left(\frac{-2}{29} \right)=(-1)^{14}(-1)^{105}=-1. \ \Box
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