# Category:Definitions/Strong Fibonacci Pseudoprimes

This category contains definitions related to Strong Fibonacci Pseudoprimes.
Related results can be found in Category:Strong Fibonacci Pseudoprimes.

A strong Fibonacci pseudoprime is a Carmichael number which also satisfies one of the following conditions:

### Type I

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 $4 m + 1$

### Type II

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:

$2 \left({p_i + 1}\right) \mathrel \backslash \left({N - p_i}\right)$ for all $p_i$

## Pages in category "Definitions/Strong Fibonacci Pseudoprimes"

The following 4 pages are in this category, out of 4 total.