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
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