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Title: Short remark on Fibonacci-Wieferich primes (English)
Author: Klaška, Jiří
Language: English
Journal: Acta Mathematica Universitatis Ostraviensis
ISSN: 1214-8148
Volume: 15
Issue: 1
Year: 2007
Pages: 21-25
Summary lang: English
Category: math
Summary: This paper has been inspired by the endeavour of a large number of mathematicians to discover a Fibonacci-Wieferich prime. An exhaustive computer search has not been successful up to the present even though there exists a conjecture that there are infinitely many such primes. This conjecture is based on the assumption that the probability that a prime $p$ is Fibonacci-Wieferich is equal to $1/p$. According to our computational results and some theoretical consideratons, another form of probability can be assumed. This observation leads us to interesting consequences. (English)
Keyword: Fibonacci-Wieferich primes
Keyword: heuristics on distributions of primes with arithmetic constraints
Keyword: Fibonacci numbers
Keyword: Wall-Sun-Sun prime
Keyword: modular periodicity
Keyword: periodic sequence
MSC: 11A07
MSC: 11B39
MSC: 11B50
MSC: 11Y99
idZBL: Zbl 1203.11021
idMR: MR2418779
Date available: 2009-12-29T09:22:25Z
Last updated: 2015-03-15
Stable URL:
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