Article
Full entry |
PDF
(0.2 MB)
Feedback
PDF
(0.2 MB)
Feedback
Keywords:
Lucas number; factoriangular number
Lucas number; factoriangular number
Summary:
We show that the only Lucas numbers which are factoriangular are $1$ and $2$.
References:
[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. MR 3248227 | Zbl 1358.11026
[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. DOI 10.1006/jnth.1996.0152 | MR 1423057 | Zbl 0870.11045
[3] Bugeaud, Y., Luca, F., Mignotte, M., Siksek, S.: Almost powers in the Lucas sequence. J. Théor. Nombres Bordx. 20 (2008), 555-600. DOI 10.5802/jtnb.642 | MR 2523309 | Zbl 1204.11030
[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.
[5] Ruiz, C. A. Gómez, Luca, F.: Fibonacci factoriangular numbers. Indag. Math., New Ser. 28 (2017), 796-804. DOI 10.1016/j.indag.2017.05.002 | MR 3679743 | Zbl 1373.11011
[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). DOI 10.1002/9781118033067 | MR 1855020 | Zbl 0984.11010
[7] Luca, F., Odjoumani, J., Togbé, A.: Pell factoriangular numbers. (to appear) in Publ. Inst. Math. Beograd, N.S. MR 3956571
[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. DOI 10.1007/978-94-011-3586-3_26 | MR 1193719 | Zbl 0749.11016
[9] Robbins, H.: A remark on Stirling's formula. Am. Math. Mon. 62 (1955), 26-29. DOI 10.2307/2308012 | MR 0069328 | Zbl 0068.05404
Search
Partner of
