USING FIBONACCI FACTORS TO CREATE FIBONACCI PSEUDOPRIMES

Carmichael showed for sufficiently large L, FL has at least one prime divisor p such that p ≡ ±1(mod L). For a given FL, we will show that a product of distinct odd prime divisors with this congruence condition is a Fibonacci pseudoprime. As a byproduct, this result leads to a proof of the presumably known result that if L is prime and FL is composite, then FL 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 n such that n ≡ ±2(mod 5) and is also a base-2 pseudoprime.