Definitions

# 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
$U\left(P,Q\right)$

with

$U_0=0, U_1=1, D=P^2-4Q$,

such that

$\left(N,D\right)=1$

and the rank appearance of N in the sequence $U\left(P,Q\right)$ is

$\left(1/a\right)\left(N-\left(D/N\right)\right)$,

where

$\left(D/N\right)$

is the Jacobi symbol.

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