Article
Full entry |
PDF
(0.2 MB)
Feedback
PDF
(0.2 MB)
Feedback
Keywords:
Fibonacci numbers; Wall's question; Wall-Sun-Sun prime; Fibonacci-Wieferich prime; modular periodicity; periodic sequence
Fibonacci numbers; Wall's question; Wall-Sun-Sun prime; Fibonacci-Wieferich prime; modular periodicity; periodic sequence
Summary:
In this paper we find certain equivalent formulations of Wall's question and derive two interesting criteria that can be used to resolve this question for particular primes.
References:
[1] Crandall, R., Dilcher, K., Pomerance, C.: A search for Wieferich and Wilson primes. Math. Comp. 66 (1997), 443-449. DOI 10.1090/S0025-5718-97-00791-6 | MR 1372002 | Zbl 0854.11002
[2] Elsenhans, A.-S., Jahnel, J.: The Fibonacci sequence modulo $p^2$---An investigation by computer for $p<10^{14}$. The On-Line Encyclopedia of Integer Sequences (2004), 27.
[3] Li, H. Ch.: Fibonacci primitive roots and Wall's question. Fibonacci Quart. 37 (1999), 77-84. MR 1676707 | Zbl 0936.11011
[4] McIntosh, R. J., Roettger, E. L.: A search for Fibonacci-Wieferich and Wolstenholme primes. Math. Comp. 76 (2007), 2087-2094. DOI 10.1090/S0025-5718-07-01955-2 | MR 2336284 | Zbl 1139.11003
[5] Sun, Z.-H., Sun, Z.-W.: Fibonacci numbers and Fermat's Last Theorem. Acta Arith. 60 (1992), 371-388. DOI 10.4064/aa-60-4-371-388 | MR 1159353 | Zbl 0725.11009
[6] Wall, D. D.: Fibonacci series modulo $m$. Amer. Math. Monthly 67 6 (1960), 525-532. DOI 10.2307/2309169 | MR 0120188 | Zbl 0101.03201
[7] Williams, H. C.: A Note on the Fibonacci quotient $F_{p-\varepsilon}/p$. Canad. Math. Bull. 25 (1982), 366-370. DOI 10.4153/CMB-1982-053-0 | MR 0668957
Search
Partner of
