| Title:
|
Tribonacci modulo $p^t$ (English) |
| Author:
|
Klaška, Jiří |
| Language:
|
English |
| Journal:
|
Mathematica Bohemica |
| ISSN:
|
0862-7959 (print) |
| ISSN:
|
2464-7136 (online) |
| Volume:
|
133 |
| Issue:
|
3 |
| Year:
|
2008 |
| Pages:
|
267-288 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Our research was inspired by the relations between the primitive periods of sequences obtained by reducing Tribonacci sequence by a given prime modulus $p$ and by its powers $p^t$, which were deduced by M. E. Waddill. In this paper we derive similar results for the case of a Tribonacci sequence that starts with an arbitrary triple of integers. (English) |
| Keyword:
|
Tribonacci |
| Keyword:
|
modular periodicity |
| Keyword:
|
periodic sequence |
| MSC:
|
11B39 |
| MSC:
|
11B50 |
| idZBL:
|
Zbl 1174.11021 |
| idMR:
|
MR2494781 |
| DOI:
|
10.21136/MB.2008.140617 |
| . |
| Date available:
|
2010-07-20T17:29:32Z |
| Last updated:
|
2020-07-29 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/140617 |
| . |
| Reference:
|
[1] Elia, M.: Derived sequences, the Tribonacci recurrence and cubic forms.The Fibonacci Quarterly 39.2 (2001), 107-115. Zbl 1001.11008, MR 1829520 |
| Reference:
|
[2] Klaška, J.: Tribonacci modulo $2^t$ and $11^t$.(to appear) in Math. Bohem. |
| Reference:
|
[3] Klaška, J.: Tribonacci partition formulas modulo $m$.Preprint (2007). MR 2591606 |
| Reference:
|
[4] 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:
|
[5] Vince, A.: Period of a linear recurrence.Acta Arith. 39 (1981), 303-311. Zbl 0396.12001, MR 0640918, 10.4064/aa-39-4-303-311 |
| Reference:
|
[6] Waddill, M. E.: Some properties of a generalized Fibonacci sequence modulo $m$.The Fibonacci Quarterly 16 4 (Aug. 1978) 344-353. Zbl 0394.10007, MR 0514322 |
| Reference:
|
[7] Wall, D. D.: Fibonacci series modulo $m$.Amer. Math. Monthly 67 6 (1960), 525-532. Zbl 0101.03201, MR 0120188, 10.1080/00029890.1960.11989541 |
| . |
