If $\alpha \in \mathbb{Z}(\omega)$, show that $\alpha$ is congruent to either $0, 1$ or $-1$ modulo $1-\omega$.
Exercise 1 page 134 in the book 'A Classical Introduction to Modern Number Theory' of K. Ireland and M. Rosen.
Thanks a lot.
If $\alpha \in \mathbb{Z}(\omega)$, show that $\alpha$ is congruent to either $0, 1$ or $-1$ modulo $1-\omega$.
Exercise 1 page 134 in the book 'A Classical Introduction to Modern Number Theory' of K. Ireland and M. Rosen.
Thanks a lot.