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.

Applications[edit]

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.

See Also[edit]

Lawrence Somer, in his 1985 thesis, also defined the Somer d-pseudoprimes. They are described in brief on page 117 of Ribenbaum 1996.

References[edit]