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Number theory Extensions

  1. Mar 21, 2010 #1
    bi9ljr.jpg

    Wouldn't mind a hint on how to start part iii), thanks.

    edit: in my notes i have for a similar question:

    'L=Q(20.5, 30.5)
    F=Q(60.5)

    degree of the min polynomial = 2, because L=F(a) and [L:F]=2
    ' (a = alpha)

    Could someone clarify what L=F(a) means so I can understand the example? Thanks
     
    Last edited: Mar 21, 2010
  2. jcsd
  3. Mar 21, 2010 #2
  4. Mar 22, 2010 #3
    The answer to the question in your second post is that you may use either expression for the reason you gave ("... both give you a poly of degree 4"). In fact, they give you the same poly. Does that clear up your original question?

    Petek
     
  5. Mar 22, 2010 #4
    Do they give the same poly?

    If I do it that way I get

    u - 20.5 = i

    u2 - 2u20.5 - 2 = -1

    u2 - 1 = 2u20.5

    u4 - 2u2 + 1 = 8u2

    u4 - 10u2 + 1 = 0

    and their answer was

    u4 - 2u2 + 9 = 0


    Hence I have two different polynomials for the question I'm trying to do, both degree 4 and monic and I'm not sure which to choose.
     
  6. Mar 22, 2010 #5
    In your calculation, this step

    u2 - 2u20.5 - 2 = -1

    is incorrect. Do you see why?

    Petek
     
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