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Title: Criteria for testing Wall's question (English)
Author: Klaška, Jiří
Language: English
Journal: Czechoslovak Mathematical Journal
ISSN: 0011-4642 (print)
ISSN: 1572-9141 (online)
Volume: 58
Issue: 4
Year: 2008
Pages: 1241-1246
Summary lang: English
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Category: math
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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. (English)
Keyword: Fibonacci numbers
Keyword: Wall's question
Keyword: Wall-Sun-Sun prime
Keyword: Fibonacci-Wieferich prime
Keyword: modular periodicity
Keyword: periodic sequence
MSC: 11A07
MSC: 11B39
MSC: 11B50
idZBL: Zbl 1174.11020
idMR: MR2471180
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Date available: 2010-07-21T08:17:24Z
Last updated: 2016-04-07
Stable URL: http://hdl.handle.net/10338.dmlcz/140454
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Reference: [1] Crandall, R., Dilcher, K., Pomerance, C.: A search for Wieferich and Wilson primes.Math. Comp. 66 (1997), 443-449. Zbl 0854.11002, MR 1372002, 10.1090/S0025-5718-97-00791-6
Reference: [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.
Reference: [3] Li, H. Ch.: Fibonacci primitive roots and Wall's question.Fibonacci Quart. 37 (1999), 77-84. Zbl 0936.11011, MR 1676707
Reference: [4] McIntosh, R. J., Roettger, E. L.: A search for Fibonacci-Wieferich and Wolstenholme primes.Math. Comp. 76 (2007), 2087-2094. Zbl 1139.11003, MR 2336284, 10.1090/S0025-5718-07-01955-2
Reference: [5] Sun, Z.-H., Sun, Z.-W.: Fibonacci numbers and Fermat's Last Theorem.Acta Arith. 60 (1992), 371-388. Zbl 0725.11009, MR 1159353
Reference: [6] Wall, D. D.: Fibonacci series modulo $m$.Amer. Math. Monthly 67 6 (1960), 525-532. Zbl 0101.03201, MR 0120188, 10.2307/2309169
Reference: [7] Williams, H. C.: A Note on the Fibonacci quotient $F_{p-\varepsilon}/p$.Canad. Math. Bull. 25 (1982), 366-370. MR 0668957, 10.4153/CMB-1982-053-0
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