# Category:Strong Fibonacci Pseudoprimes

Jump to navigation
Jump to search

This category contains results about Strong Fibonacci Pseudoprimes.

Definitions specific to this category can be found in Definitions/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 "Strong Fibonacci Pseudoprimes"

This category contains only the following page.