Research article

Identities concerning k-balancing and k-Lucas-balancing numbers of arithmetic indexes

  • Received: 08 January 2019 Accepted: 08 March 2019 Published: 28 March 2019
  • In this article, we derive some identities involving $k$ balancing and $k$-Lucas-balancing numbers of arithmetic indexes, say $an+p$, where $a$ and $p$ are some fixed integers with $0\leq p\leq a-1.$

    Citation: Prasanta Kumar Ray. Identities concerning k-balancing and k-Lucas-balancing numbers of arithmetic indexes[J]. AIMS Mathematics, 2019, 4(2): 308-315. doi: 10.3934/math.2018.2.308

    Related Papers:

  • In this article, we derive some identities involving $k$ balancing and $k$-Lucas-balancing numbers of arithmetic indexes, say $an+p$, where $a$ and $p$ are some fixed integers with $0\leq p\leq a-1.$


    加载中


    [1] A. Behera and G. K. Panda, On the square roots of triangular numbers, Fibonacci Quart., 37 (1999), 98–105.
    [2] A. Berczes, K. Liptai and I. Pink, On generalized balancing sequences, Fibonacci Quart., 48 (2010), 121–128.
    [3] R. P. Finkelstein, The house problem, Amer. Math. Monthly, 72 (1965), 1082–1088.
    [4] T. Komatsu and L. Szalay, Balancing with binomial coefficients, Int. J. Number Theory, 10 (2014), 1729–1742.
    [5] K. Liptai, Fibonacci balancing numbers, Fibonacci Quart., 42 (2004), 330–340.
    [6] K. Liptai, F. Luca, Á. Pintér and L. Szalay, Generalized balancing numbers, Indagat. Math., 20 (2009), 87–100.
    [7] G. K. Panda, Some fascinating properties of balancing numbers, In Proc. of Eleventh Internat. Conference on Fibonacci Numbers and Their Applications, Cong. Numerantium, 194 (2009), 185–189.
    [8] B. K. Patel, N. Irmak and P. K. Ray, Incomplete balancing and Lucas-balancing numbers, Math. Rep., 20 (2018), 59–72.
    [9] P. K. Ray, On the properties of k-balancing and k-Lucas-balancing numbers, Acta Commentat. Univ. Tartu. Math., 21 (2017), 259–274.
    [10] P. K. Ray, Balancing polynomials and their derivatives, Ukr. Math. J., 69 (2017), 646–663.
  • Reader Comments
  • © 2019 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)
通讯作者: 陈斌, bchen63@163.com
  • 1. 

    沈阳化工大学材料科学与工程学院 沈阳 110142

  1. 本站搜索
  2. 百度学术搜索
  3. 万方数据库搜索
  4. CNKI搜索

Metrics

Article views(3476) PDF downloads(559) Cited by(2)

Article outline

Other Articles By Authors

/

DownLoad:  Full-Size Img  PowerPoint
Return
Return

Catalog