Strong Frobenius Pseudoprime

A Pseudoprime which obeys an additional restriction beyond that required for a Frobenius Pseudoprime. A number $n$ with $(n,2a)=1$ is a strong Frobenius pseudoprime with respect to $x-a$ Iff $n$ is a Strong Pseudoprime with respect to $f(x)$. Every strong Frobenius pseudoprime with respect to $x-a$ is an Euler Pseudoprime to the base $a$.

Every strong Frobenius pseudoprime with respect to $f(x)=x^2-bx-c$ such that $((b^2+4c)/n)=-1$ is a Strong Lucas Pseudoprime with parameters $(b,c)$. Every strong Frobenius pseudoprime $n$ with respect to $x^2-bx+1$ is an Extra Strong Lucas Pseudoprime to the base $b$.

See also Frobenius Pseudoprime

References

Grantham, J. ``Frobenius Pseudoprimes.'' 1996. http://www.clark.net/pub/grantham/pseudo/pseudo1.ps