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Homework Help: Help me construcing finite field, !

  1. Jan 15, 2008 #1
    Help me construcing finite field, plz!

    I need Construct a finite field with q Elements (10^9<q<10^10) and find
    a primitive root. That should be done in mathematica but I should not use Package for Finite Fields.

    Any idea how to solve this problem?
  2. jcsd
  3. Jan 15, 2008 #2


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    What do you know about fields?
    Do you have any examples of fields?
  4. Jan 15, 2008 #3
    I don’t think this is pre-calc, but:

    Can you think of a number p and n where

    10^9 < p^n < 10^10

    you should know how to construct a field with p^n elements.

    Hint: It involves Z_p and a irreducible polynomial of order n (check your class notes!)

    Edit: p must be prime of course
    Last edited: Jan 15, 2008
  5. Jan 16, 2008 #4
    Thank you very much!

    Could you refer me to any tutorial for constructing field with p^n elements the?
    I am not good with fields at all!

    When I construct the field do I have to take all polynomials possible of n degree in Z/Zp or only one irreducible or all irreducible ones?

    I don't have clear what is the finite field. What do I have to find in order to construct finite field?
    Last edited: Jan 16, 2008
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