Somer-Lucas pseudoprime

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

<math>U(P,Q)<math>

with

<math>U_0=0, U_1=1, D=P^2–4Q<math>,

such that

<math>(N,D)=1<math>

and the rank appearance of N in the sequence <math>U(P,Q)<math> is

<math>(1/a)(N-(D/N))<math>,

where

<math>(D/N)<math>

is the Jacobi symbol.