Definition:Strong Fibonacci Pseudoprime/Type I

Definition
A strong Fibonacci pseudoprime of type I is a Carmichael number $N = \displaystyle \prod p_i$ such that an even number of the prime factors $p_i$ are of the form $4 m - 1$ where:
 * $(1): \quad 2 \left({p_i + 1}\right) \mathrel \backslash \left({N - 1}\right)$ for those $p_i$ of the form $4 m - 1$
 * $(2): \quad \left({p_i + 1}\right) \mathrel \backslash \left({N \pm 1}\right)$ for those $p_i$ of the form $4 m + 1$

where:
 * $N = \displaystyle \prod p_i$ is the prime decomposition of $N$
 * $\backslash$ denotes divisibility.