Somer-Lucas pseudoprime

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In mathematics, in particular number theory, an odd composite number N is a Somer-Lucas d-pseudoprime (with given d1) if there exists a nondegenerate Lucas sequence

U(P,Q)

with

U₀ = 0,U₁ = 1,D = P² − 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.