A Pseudoprime which obeys an additional restriction beyond that required for a Frobenius Pseudoprime. A number with is a strong Frobenius pseudoprime with respect to Iff is a Strong Pseudoprime with respect to . Every strong Frobenius pseudoprime with respect to is an Euler Pseudoprime to the base .
Every strong Frobenius pseudoprime with respect to such that is a Strong Lucas Pseudoprime with parameters . Every strong Frobenius pseudoprime with respect to is an Extra Strong Lucas Pseudoprime to the base .
See also Frobenius Pseudoprime
References
Grantham, J. ``Frobenius Pseudoprimes.'' 1996.
http://www.clark.net/pub/grantham/pseudo/pseudo1.ps