| 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 |
| . |
| Category:
|
math |
| . |
| 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 |
| . |
| Date available:
|
2010-07-21T08:17:24Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/140454 |
| . |
| 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, 10.4064/aa-60-4-371-388 |
| 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 |
| . |
