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Sylvester Cyclotomic Number

Given a Lucas Sequence with parameters $P$ and $Q$, discriminant $D\not=0$, and roots $\alpha$ and $\beta$, the Sylvester cyclotomic numbers are

Q_n=\prod_r (\alpha-\zeta^r \beta),


\zeta\equiv \cos\left({2\pi\over n}\right)+i\sin\left({2\pi\over n}\right)

is a Primitive Root of Unity and the product is over all exponents $r$ Relatively Prime to $n$ such that $r\in [1,n).$

See also Lucas Sequence


Ribenboim, P. The Book of Prime Number Records, 2nd ed. New York: Springer-Verlag, p. 69, 1989.

© 1996-9 Eric W. Weisstein