Euler-Lucas Pseudoprime

Let  and  be Lucas sequences generated by  and , and define

(1)

Then

(2)

where  is the Legendre symbol. An odd composite number  such that  (i.e.,  and  are relatively prime) is called an Euler-Lucas pseudoprime with parameters .

REFERENCES:

Ribenboim, P. "Euler-Lucas Pseudoprimes (elpsp()) and Strong Lucas Pseudoprimes (slpsp())." §2.X.C in The New Book of Prime Number Records. New York: Springer-Verlag, pp. 130-131, 1996.