Help finding units in a ring

  • Thread starter Jupiter
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  • #1
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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.
 
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Answers and Replies

  • #2
46
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I got it! I needed part b. I was going about the problem the wrong way. Thanks anyway!
 

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