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/course.../home/hw12.pdf
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.