Somer–Lucas pseudoprime - Alchetron, the free social encyclopedia

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 − 4 Q , such that gcd ( N , D ) = 1 and the rank appearance of N in the sequence U(P, Q) is

1 d ( N − ( D N ) ) ,

where ( D N ) is the Jacobi symbol.

Applications

Unlike the standard Lucas pseudoprimes, there is no known efficient primality test using the Lucas d-pseudoprimes. Hence they are not generally used for computation.

References

Somer–Lucas pseudoprime Wikipedia

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