prove that the set of algebraic integers in$\mathbb{Q}[\zeta_p]$ are exactly $\mathbb{Z}[\zeta_p]$where $\zeta_p$ is a primitive p-th root of unity(may assume p is prime)
I'm sure that the problem is solvable when p is prime(also, in this case the question seems easier )
I have tried to solve this problem by using Galois group，but it turned out that the proof is incorrect. I think I need to change my method but I have no idea about it
Aany advice will be helpful,Thank you.