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 
.
