  Carmichael showed for sufficiently large $L$, that $F_L$ has at least one
prime divisor that is $\pm 1({\rm mod}\, L)$. For a given $F_L$, we will show
that a product of distinct odd prime divisors with that congruence condition is
a Fibonacci pseudoprime. Such pseudoprimes can be used in an attempt, here
unsuccessful, to find an example of a Baillie-PSW pseudoprime, i.e.\ an odd
Fibonacci pseudoprime that is congruent to $\pm 2({\rm mod}\, 5)$ and is also a
base-2 pseudoprime.
