# 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 $N = \ds \prod p_i$ such that an even number of the prime factors $p_i$ are of the form $4 m - 1$ where:

 $\text {(1)}: \quad$ $\ds 2 \paren {p_i + 1}$ $\divides$ $\ds \paren {N - 1}$ for those $p_i$ of the form $4 m - 1$ $\text {(2)}: \quad$ $\ds \paren {p_i + 1}$ $\divides$ $\ds \paren {N \pm 1}$ for those $p_i$ of the form $4 m + 1$

### Type II

A strong Fibonacci pseudoprime of type II is a Carmichael number $N = \ds \prod p_i$ 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 $p_i$

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

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