Somer-Lucas pseudoprime

In mathematics, in particular number theory, an odd composite number "N" is a Somer-Lucas "d"-pseudoprime (with given d$le$1) if there exists a nondegenerate Lucas sequence :$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

:$(D/N)$

is the Jacobi symbol.