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

Voir la notice de l'article provenant de la source Czech Digital Mathematics Library

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 
@article{COMIM_2007__15_1_a3,
     author = {Kla\v{s}ka, Ji\v{r}{\'\i}},
     title = {Short remark on {Fibonacci-Wieferich} primes},
     journal = {Communications in Mathematics},
     pages = {21--25},
     publisher = {mathdoc},
     volume = {15},
     number = {1},
     year = {2007},
     mrnumber = {2418779},
     zbl = {1203.11021},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/COMIM_2007__15_1_a3/}
}
TY  - JOUR
AU  - Klaška, Jiří
TI  - Short remark on Fibonacci-Wieferich primes
JO  - Communications in Mathematics
PY  - 2007
SP  - 21
EP  - 25
VL  - 15
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/COMIM_2007__15_1_a3/
LA  - en
ID  - COMIM_2007__15_1_a3
ER  - 
%0 Journal Article
%A Klaška, Jiří
%T Short remark on Fibonacci-Wieferich primes
%J Communications in Mathematics
%D 2007
%P 21-25
%V 15
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/COMIM_2007__15_1_a3/
%G en
%F COMIM_2007__15_1_a3
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/