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Re: Algebraic comments

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  • mikeoakes2
    ... If d = 1 mod 4, then the integers of the field k(sqrt(d)) are indeed of your form but you must also allow A and B to be both half-integers. See for example
    Message 1 of 3 , Dec 4, 2009
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      --- In primenumbers@yahoogroups.com, Kermit Rose <kermit@...> wrote:
      >
      >
      > Primes in algebraic number systems:
      >
      > Consider the extension to the integers,
      >
      > {A + B * sqrt(d) }, where A, B are variable integers, and d is a
      > fixed integer.

      If d = 1 mod 4, then the integers of the field k(sqrt(d)) are indeed of your form but you must also allow A and B to be both half-integers.
      See for example Hardy & Wright, Theorem 238.

      Mike
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