Geodesic
Short remark on Fibonacci-Wieferich primes
Communications in Mathematics, Tome 15 (2007) no. 1, pp. 21-25 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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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.
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.
Classification : 11A07, 11B39, 11B50, 11Y99
Keywords: Fibonacci-Wieferich primes; heuristics on distributions of primes with arithmetic constraints; Fibonacci numbers; Wall-Sun-Sun prime; modular periodicity; periodic sequence 
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Klaška, Jiří. Short remark on Fibonacci-Wieferich primes. Communications in Mathematics, Tome 15 (2007) no. 1, pp. 21-25. http://geodesic.mathdoc.fr/item/COMIM_2007_15_1_a3/

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