# Help finding units in a ring

1. Apr 13, 2004

### Jupiter

How can I show that if
$$\frac{a}{a^2-2b^2},\frac{b}{a^2-2b^2}\in \mathbb{Z}$$

then $$a^2-2b^2=\pm 1$$?
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. Apr 13, 2004

### Jupiter

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