Category:Definitions/Strong Fibonacci Pseudoprimes

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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:

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


Type II

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

Pages in category "Definitions/Strong Fibonacci Pseudoprimes"

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