Definition:Strong Fibonacci Pseudoprime/Type I

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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:

\(\text {(1)}: \quad\) \(\displaystyle 2 \paren {p_i + 1}\) \(\divides\) \(\displaystyle \paren {N - 1}\) 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 $4 m + 1$

where:

$N = \displaystyle \prod p_i$ is the prime decomposition of $N$
$\divides$ denotes divisibility.


Source of Name

This entry was named for Leonardo Fibonacci.


Sources