Somer–Lucas pseudoprime

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(P, Q) is

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

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

References

• Weisstein, Eric W., "Somer–Lucas Pseudoprime" from MathWorld.
• Ribenboim, P. (1996). "§2.X.D Somer-Lucas Pseudoprimes". The New Book of Prime Number Records (3rd ed. ed.). New York: Springer-Verlag. pp. 131–132. http://books.google.com/books?id=72eg8bFw40kC&pg=PA131.