Lehmer Number

A Lehmer number is 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 not a root of unity. Then the corresponding 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 New Book of Prime Number Records. New York: Springer-Verlag, pp. 61 and 70, 1989.

Shorey, T. N. and Stewart, C. L. "On Divisors of Fermat, Fibonacci, Lucas and Lehmer Numbers, 2." J. London Math. Soc. 23, 17-23, 1981.

Stewart, C. L. "On Divisors of Fermat, Fibonacci, Lucas and Lehmer Numbers." Proc. London Math. Soc. 35, 425-447, 1977.

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