| Title:
|
Lucas factoriangular numbers (English) |
| Author:
|
Kafle, Bir |
| Author:
|
Luca, Florian |
| Author:
|
Togbé, Alain |
| Language:
|
English |
| Journal:
|
Mathematica Bohemica |
| ISSN:
|
0862-7959 (print) |
| ISSN:
|
2464-7136 (online) |
| Volume:
|
145 |
| Issue:
|
1 |
| Year:
|
2020 |
| Pages:
|
33-43 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We show that the only Lucas numbers which are factoriangular are $1$ and $2$. (English) |
| Keyword:
|
Lucas number |
| Keyword:
|
factoriangular number |
| MSC:
|
11A25 |
| MSC:
|
11B39 |
| MSC:
|
11J86 |
| idZBL:
|
07217178 |
| idMR:
|
MR4088691 |
| DOI:
|
10.21136/MB.2018.0021-18 |
| . |
| Date available:
|
2020-03-12T08:19:03Z |
| Last updated:
|
2020-11-18 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/148062 |
| . |
| Reference:
|
[1] Bravo, J. J., Luca, F.: Powers of two as sums of two Lucas numbers.J. Integer Seq. 17 (2014), Article No. 14.8.3, 12 pages. Zbl 1358.11026, MR 3248227 |
| Reference:
|
[2] Bugeaud, Y., Laurent, M.: Effective lower bound for the $p$-adic distance between powers of algebraic numbers.J. Number Theory 61 (1996), 311-342 French. Zbl 0870.11045, MR 1423057, 10.1006/jnth.1996.0152 |
| Reference:
|
[3] Bugeaud, Y., Luca, F., Mignotte, M., Siksek, S.: Almost powers in the Lucas sequence.J. Théor. Nombres Bordx. 20 (2008), 555-600. Zbl 1204.11030, MR 2523309, 10.5802/jtnb.642 |
| Reference:
|
[4] Castillo, R. C.: On the sum of corresponding factorials and triangular numbers: Some preliminary results.Asia Pac. J. Multidisciplinary Research 3 (2015), 5-11. |
| Reference:
|
[5] Ruiz, C. A. Gómez, Luca, F.: Fibonacci factoriangular numbers.Indag. Math., New Ser. 28 (2017), 796-804. Zbl 1373.11011, MR 3679743, 10.1016/j.indag.2017.05.002 |
| Reference:
|
[6] Koshy, T.: Fibonacci and Lucas Numbers with Applications.Pure and Applied Mathematics. A Wiley-Interscience Series of Texts, Monographs, and Tracts. Wiley-Interscience, New York (2001). Zbl 0984.11010, MR 1855020, 10.1002/9781118033067 |
| Reference:
|
[7] Luca, F., Odjoumani, J., Togbé, A.: Pell factoriangular numbers.(to appear) in Publ. Inst. Math. Beograd, N.S. MR 3956571 |
| Reference:
|
[8] Ming, L.: On triangular Lucas numbers.Applications of Fibonacci Numbers. Vol. 4. Proc. 4th Int. Conf. on Fibonacci Numbers and Their Applications, Wake Forest University, Winston-Salem, USA, 1990 Kluwer Academic Publishers, Dordrecht (1991), 231-240 G. E. Bergun et al. Zbl 0749.11016, MR 1193719, 10.1007/978-94-011-3586-3_26 |
| Reference:
|
[9] Robbins, H.: A remark on Stirling's formula.Am. Math. Mon. 62 (1955), 26-29. Zbl 0068.05404, MR 0069328, 10.2307/2308012 |
| . |
