## Lehmer Number

A number generated by a generalization of a Lucas Sequence. Let and be Complex Numbers with

 (1)

 (2)

where and are Relatively Prime Nonzero Integers and is a Root of Unity. Then the Lehmer numbers are
 (3)

and the companion numbers
 (4)

References

Lehmer, D. H. An Extended Theory of Lucas' Functions.'' Ann. Math. 31, 419-448, 1930.

Ribenboim, P. The Book of Prime Number Records, 2nd ed. New York: Springer-Verlag, pp. 61 and 70, 1989.

Williams, H. C. The Primality of .'' Canad. Math. Bull. 15, 585-589, 1972.