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Primitive Root of Unity

  1. Apr 30, 2014 #1
    1. The problem statement, all variables and given/known data
    In F17, 2 is a primitive 8th root of unity. Evaluate f(x) = 7x3+8x2+3x+5 at the eight powers of 2 in F17. Verify that the method requires at most 16 multiplications in F17.


    2. Relevant equations
    You can can more clearly see the theorem on page 376-378 and the problem is on page 382 #6:
    http://igortitara.files.wordpress.com/2010/04/a-concrete-introduction-to-higher-algebra1.pdf


    3. The attempt at a solution
    I was able to find that the d=3, but am unclear on how I evaluate f(x) based of Theorem 3.
     
    Last edited: Apr 30, 2014
  2. jcsd
  3. Apr 30, 2014 #2

    Zondrina

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    Homework Helper

    The question states that ##2## is a primitive ##2^3##'th root of unity, that is ##2^8 = e = 1##.

    You need to evaluate ##f(2), f(2^2), f(2^3), ... , f(2^8)##. This requires at most ##2^r(r-1)## multiplications, which works out to:

    ##2^r(r-1) = 2^3(3-1) = 8(2) = 16##
     
    Last edited: Apr 30, 2014
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