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Are these two fields equal

  1. Apr 13, 2005 #1
    Hey,
    Does anyone know how to show that these fields are equal:
    [tex]Q(\sqrt{p_1},\sqrt{p_2},...,\sqrt{p_k})=Q(\sqrt{p_1}+\sqrt{p_2}+...+\sqrt{p_k})[/tex],
    where [tex]p_1,...,p_k[/tex] are distinct primes in Z.

    One inclusion is clear to me, but i'm having problems showing they're equal. Thanks!
     
  2. jcsd
  3. Apr 13, 2005 #2

    Hurkyl

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    Induction on k, maybe?
     
  4. Apr 13, 2005 #3
    Right....note to self, always remember about induction. Thank you.
    (although my solution using induction looks super messy)
     
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