On the Lucas sequence equation 1/Un = Σk=1∞ Uk-1/xk

被引：0
|
作者：
Tengely, Szabolcs [1 ]
机构：
[1] Univ Derecen, Math Inst, H-4010 Debrecen, Hungary
来源：
PERIODICA MATHEMATICA HUNGARICA | 2015年 / 71卷 / 02期
关键词：
Lucas sequences; Diophantine equations; Elliptic curves; ELLIPTIC DIOPHANTINE EQUATIONS; ESTIMATING LINEAR-FORMS; INTEGER SOLUTIONS; FRACTIONS;
D O I：
10.1007/s10998-015-0101-4
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In 1953 Stancliff noted an interesting property of the Fibonacci number F-11 = 89. One has that 1/89 = 0/10 + 1/10(2) + 1/10(3) + 2/10(4) + 3/10(5) + 5/10(6) + ..., where in the numerators the elements of the Fibonacci sequence appear. We provide methods to determine similar identities in case of Lucas sequences. As an example we prove that 1/U-10 = 1/416020 = Sigma(infinity)(k=0) U-k/647(k+1), where U-0 = 0, U-1 = 1 and U-n = 4U(n-1) + Un-2, n >= 2.
引用
收藏
页码：236 / 242
页数：7
相关论文
共 50 条
  • [1] On the Solutions of the Lucas Sequence Equation ± 1/Vn(P2, Q2) = Σk=1∞ Uk-1(P1,Q1)/xk
    Abdulzahra, A. A.
    Hashim, H. R.
    MALAYSIAN JOURNAL OF MATHEMATICAL SCIENCES, 2024, 18 (02): : 357 - 369
  • [2] The total synthesis of UK-1
    DeLuca, MR
    Kerwin, SM
    TETRAHEDRON LETTERS, 1997, 38 (02) : 199 - 202
  • [3] On the equation 1k+2k + ... + xk=yn
    Györy, K
    Pintér, A
    PUBLICATIONES MATHEMATICAE-DEBRECEN, 2003, 62 (3-4): : 403 - 414
  • [4] REMARKS ON THE EQUATION 1K+2K+=+(X-1)K=XK
    URBANOWICZ, J
    PROCEEDINGS OF THE KONINKLIJKE NEDERLANDSE AKADEMIE VAN WETENSCHAPPEN SERIES A-MATHEMATICAL SCIENCES, 1988, 91 (03): : 343 - 348
  • [5] A note on the Diophantine equation (xk - 1)(yk - 1)2 = z k - 1
    Li, Yangcheng
    NOTES ON NUMBER THEORY AND DISCRETE MATHEMATICS, 2024, 30 (04) : 825 - 831
  • [6] REAL ROOTS OF EQUATION (X-1)K=XK-1
    SMITH, DA
    AMERICAN MATHEMATICAL MONTHLY, 1966, 73 (07): : 754 - &
  • [7] CORROSION INDICATING EQUIPMENT UK-1
    GERASIMENKO, YS
    SOROKIN, VI
    RUDENKO, AK
    ABROSIMOV, VS
    PROTECTION OF METALS, 1986, 22 (02): : 265 - 268
  • [8] On the Diophantine equation (x-1)k + xk + (x+1)k = yn
    Zhang, Zhongfeng
    PUBLICATIONES MATHEMATICAE-DEBRECEN, 2014, 85 (1-2): : 93 - 100
  • [9] On the Diophantine equation 1k+2k +...+ xk = yn
    Bennett, MA
    Gyory, K
    Pintér, A
    COMPOSITIO MATHEMATICA, 2004, 140 (06) : 1417 - 1431
  • [10] On the equation 1k+2k + ••• + xk = yn for fixed x
    Berczes, A.
    Hajdu, L.
    Miyazaki, T.
    Pink, I.
    JOURNAL OF NUMBER THEORY, 2016, 163 : 43 - 60
12345