# Definition:Strong Fibonacci Pseudoprime/Type II

## Definition

A strong Fibonacci pseudoprime of type II is a Carmichael number $N = \displaystyle \prod p_i$ such that an odd number of the prime factors $p_i$ are of the form $4 m - 1$ where:

$2 \paren {p_i + 1} \divides \paren {N - p_i}$ for all $p_i$

where:

$N = \displaystyle \prod p_i$ is the prime decomposition of $N$
$\divides$ denotes divisibility.

## Source of Name

This entry was named for Leonardo Fibonacci.