Somer-Lucas Pseudoprime

An Odd Composite Number $N$ is called a Somer-Lucas $d$-pseudoprime (with $d\geq 1$) if there Exists a nondegenerate Lucas Sequence $U(P,Q)$ with $U_0=0$, $U_1=1$, $D=P^2-4Q$, such that $(N,D)=1$ and the rank appearance of $N$ in the sequence $U(P,Q)$ is $(1/a)(N-(D/N))$, where $(D/N)$ denotes the Jacobi Symbol.

See also Lucas Sequence, Pseudoprime

References

Ribenboim, P. ``Somer-Lucas Pseudoprimes.'' §2.X.D in The New Book of Prime Number Records, 3rd ed. New York: Springer-Verlag, pp. 131-132, 1996.