Geodesic
Short remark on Fibonacci-Wieferich primes
Communications in Mathematics, Tome 15 (2007) no. 1, pp. 21-25.

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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.
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/