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 ${\displaystyle U(P,Q)}$ with the discriminant ${\displaystyle D=P^{2}-4Q,}$ such that ${\displaystyle \gcd(N,D)=1}$ and the rank appearance of N in the sequence U(P, Q) is

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

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