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Somer-Lucas Pseudoprime


An odd composite number N is called a Somer-Lucas d-pseudoprime (with d>=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) denotes the Jacobi symbol.


See also

Lucas Sequence, Pseudoprime

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References

Ribenboim, P. "Somer-Lucas Pseudoprimes." §2.X.D in The New Book of Prime Number Records, 3rd ed. New York: Springer-Verlag, pp. 131-132, 1996.

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Somer-Lucas Pseudoprime

Cite this as:

Weisstein, Eric W. "Somer-Lucas Pseudoprime." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/Somer-LucasPseudoprime.html

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