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 d ≥ 1) if there exists a nondegenerate Lucas sequence U(P,Q) with the discriminant D=P^2-4Q, such that \gcd(N,D)=1 and the rank appearance of N in the sequence U(PQ) is

\frac{1}{d}\left(N-\left(\frac{D}{N}\right)\right),

where \left(\frac{D}{N}\right) is the Jacobi symbol.

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