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Number theory Extensions

  • Thread starter Firepanda
  • Start date
  • #1
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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:

Answers and Replies

  • #2
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  • #3
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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
 
  • #4
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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
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.
 
  • #5
362
7
In your calculation, this step

u2 - 2u20.5 - 2 = -1

is incorrect. Do you see why?

Petek
 

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