Somer–Lucas pseudoprime
In mathematics, specifically number theory, an odd and composite number N is a Somer–Lucas d-pseudoprime (with given d ≥ 1) if there exists a nondegenerate Lucas sequence U ( P , Q ) {\displaystyle U(P,Q)} with the discriminant D = P 2 − 4 Q , {\displaystyle D=P^{2}-4Q,} such that gcd ( N , D ) = 1 {\displaystyle \gcd(N,D)=1} and the rank appearance of N in the sequence U(P, Q) is 1 d ( N − ( D N ) ) , {\displaystyle {\frac {1}{d}}\left(N-\left({\frac {D}{N}}\right)\right),} where ( D N ) {\displaystyle \left({\frac {D}{N}}\right)} is the Jacobi symbol. == Applications == Unlike the standard Lucas pseudoprimes, there is no known efficient primality test using the Lucas d-pseudoprimes.