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Math Help - group problem...

  1. #1
    Junior Member
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    group problem...

    Q: in a group{1,2,.....16} under the operation of multiplication modulo 17,the order of element 3 is???
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  2. #2
    Super Member Gamma's Avatar
    Joined
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    Iowa City, IA
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    Just do it

    just multiply
    3=3 (mod 17)
    3^2=9  (mod 17)
    3^3=9*3=27 \equiv 10 (mod 17)
    3^4=10*3=30 \equiv 13 (mod 17)
    3^5=13*3=39 \equiv 5 (mod 17)
    3^6=5*3=15 \equiv -2 (mod 17)
    3^7= -2*3 = -6 (mod 17)
    3^8=-6*3 = -18 \equiv -1 (mod 17)
    3^{16}=(3^8)^2=(-1)^2=1 (mod 17)
    order is 16 if I did it all right, you can do this on your own, this says 3 is a generator for \left(\frac{\mathbb{Z}}{(17\mathbb{Z})}\right)^{\t  imes}
    Last edited by Gamma; April 21st 2009 at 09:30 PM. Reason: parenthesis mess up
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