# 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 $U(P,Q)$ 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.