I have to questions regarding UFD's.
1. Assume that Q[Sqrt(d)] is a UFD and that is an integer in Q[Sqrt(d)] where and (with a bar above it) have no common factor, but the norm of , N[ ] is a perfect square in . Can someone show that is a perfect square in the quadratic integers in Q[Sqrt(d)] ?
2. How can we prove that is a UFD?
Thank you all, I appreciate the help!