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:<math>\Phi_{pq}(z)=\frac{(z^{pq}-1) (z-1)}{(z^p-1) (z^q-1)}=\frac {\sum_{k=0}^{q-1} z^{pk} } {\sum_{k=0}^{q-1} z^k}</math>
:<math>\Phi_{pq}(z)=\frac{(z^{pq}-1) (z-1)}{(z^p-1) (z^q-1)}=\frac {\sum_{k=0}^{q-1} z^{pk} } {\sum_{k=0}^{q-1} z^k}</math>
==Galois Theory==
The Galois group associated to the nth cyclotomic polynomial is <math>(\mathbb{Z}/n\mathbb{Z})^*</math>, the group of cyclic units modulo n. Cyclotomic fields play an important part in [[algebraic number theory]] and can be used to show that certain constructions posited by ancient Greek geometers are impossible, such as trisecting the angle and constructing certain regular polygons.
[[Category:Mathematics]]
[[Category:Mathematics]]
[[category:algebra]]
[[category:algebra]]