Using Fibonacci factors to create Fibonacci pseudoprimes

2021/05/28 by Junhyun Lim, Lim, Junhyun, Shaunak Mashalkar +3
Mathematics · Physics and Astronomy · #11A51 (Secondary) #11B39 (Primary) #Advanced Mathematical Theories #Advanced Mathematical Theories and Applications #FOS: Mathematics #Mathematics and Applications #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2105.13513

openalex publication_date 2021/05/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Carmichael showed for sufficiently large L, that F_L has at least one prime divisor that is ± 1(\rm mod L). For a given F_L, we will show that a product of distinct odd prime divisors with that congruence condition is a Fibonacci pseudoprime. Such pseudoprimes can be used in an attempt, here unsuccessful, to find an example of a Baillie-PSW pseudoprime, i.e. an odd Fibonacci pseudoprime that is congruent to ± 2(\rm mod 5) and is also a base-2 pseudoprime.

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