Definition:Strong Fibonacci Pseudoprime/Type II

Definition

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 $p_i$

where:

$N = \ds \prod p_i$ is the prime decomposition of $N$

$\divides$ denotes divisibility.

Source of Name

This entry was named for Leonardo Fibonacci.

Sources

• Jul. 1993: R.G.E. Pinch: The Carmichael Numbers up to $10^{15}$ (Math. Comp. Vol. 61, no. 203: pp. 381 – 391)  www.jstor.org/stable/2152963