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Help finding units in a ring

  1. Apr 13, 2004 #1
    How can I show that if
    [tex]\frac{a}{a^2-2b^2},\frac{b}{a^2-2b^2}\in \mathbb{Z}[/tex]

    then [tex] a^2-2b^2=\pm 1[/tex]?
    If you care to see the whole problem, you can find it here:
    http://www.math.rochester.edu/courses/236H/home/hw12.pdf [Broken]
    It's #4 part c.

    BTW, why is the significance of this "norm map"? I tried to google it for fun, but couldn't find much.
    Last edited by a moderator: May 1, 2017
  2. jcsd
  3. Apr 13, 2004 #2
    I got it! I needed part b. I was going about the problem the wrong way. Thanks anyway!
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