[This question](http://mathoverflow.net/questions/139975/positivity-of-the-norm-of-an-element-of-a-cyclotomic-field) was originally asked in MSE about a year ago. Nobody has answered it. So I posted it here. I wonder why they think it's not research level. Because the question is elementary and every undergraduate student can understand what it means? I have no intention to compare my question with the FLT, but cannot resist the temptation to bring it up. Everybody understands what the FLT means. However, certainly it's research level. **EDIT** *I have no intention to compare my question with the FLT, but cannot resist the temptation to bring it up.* I would like to change this into the following statement. *I don't think my question is as imortant as the FLT, but cannot resist the temptation to bring it up.*