Definitions

somer

Somer-Lucas pseudoprime

In mathematics, in particular number theory, an odd composite number N is a Somer-Lucas d-pseudoprime (with given dle 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.

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