Let $\zeta_{39}$ be a primitive $39$th root of unity. How can I prove that all the conjugates of $\zeta_{39}$ form an integral basis of $\mathbb{Q}(\zeta_{39})$?
This is from the paper "Cyclotomic Construction of Leech's Lattice" by M. Craig. It's supposed to follow from the identity $$ \frac{ \theta^{3j} (\theta^{39}-1) }{\theta^{13} - 1} = 0 = \frac{ \theta^{} (\theta^{39}-1) }{\theta^{3} - 1}, $$ where $\theta = \zeta_{39}$ and $j \in \mathbb{Z}$. Thanks!