Here is your PDF file. Let me know if anything has to be modified.
We had the following problem for homework: let prove that lies in a cyclotomic extension.
(Without using Kronecker-Weber Theorem!)
I found a solution to this problem using quadradic Gauss sums, however this is not a course in number theory - it is a course on Galois theory, therefore my solution might be not acceptable. I will post it anyway because I want to print it out and give it to the class so which is why I am hanging it on the forum. I am interested in seeing other solutions.
Thank you very much!
There are two mistakes that I did. The first mistake appears in the proof of Theorem 1. The part in the parenthesis "If this fact is not familar ... "
After Theorem 3, "As a result ... ", that paragraph. It should say and not .
I edited my post above if it makes it any easier.
It's been a while since I've watched a football match on TV so I won't comment on this.I am sorry that France lost yesterday.