Fibonacci Pseudoprimes
A Fibonacci pseudoprime is a composite number n for which
- Vn is congruent to P modulo n
when Q = ±1.
A strong Fibonacci pseudoprime may be defined as a composite number which is a Fibonacci pseudoprime for all P. It follows (see Müller and Oswald) that in this case:
- An odd composite integer n is also a Carmichael number
- 2(pi + 1) | (n − 1) or 2(pi + 1) | (n − pi) for every prime pi dividing n.
The smallest example of a strong Fibonacci pseudoprime is 443372888629441, which has factors 17, 31, 41, 43, 89, 97, 167 and 331.
It is conjectured that there are no even Fibonacci pseudoprimes.
Read more about this topic: Lucas Pseudoprime