- Publications
- Influence

Claim Your Author Page

Ensure your research is discoverable on Semantic Scholar. Claiming your author page allows you to personalize the information displayed and manage publications.

That the ratio F kn /F n , where F n is the n-th Fibonacci number, is integral is a well-known fact. Define
$$ {R_k}(n) = \frac{{{F_{{kn}}}}}{{{F_n}}} $$
(1.1)
for all positive integral… (More)

It is well known that any positive integer n can be written uniquely in the form
$$ n = \sum\limits_{{r = 2}}^{\infty } {{{e}_{r}}{{F}_{r}}} $$
(1)
, where \( {{e}_{r}} \in \{ 0,1\}… (More)

We begin by describing an elementary process for expressing a positive proper fraction as a sum of reciprocals of positive integers. Starting with m 1/n 1, where m 1 < n 1, we subtract the largest… (More)

In this paper we show that a sequence {A n} defined by the second order recurrence relation
$$A_{n+2} = u_{1}A_{n+1} + u_2A_n$$
, satisfies the congruence relation
$$A_{n+2k} \equiv… (More)

That any positive integer N can be represented as a sum of distinct nonconsecutive Fibonacci numbers F n is a well-known fact. Apart from the equivalent use of F 2 instead of F 1, such a… (More)

Zeckendor’s Theorem guarantees that every positive integer can be uniquely expressed as a sum of Fibonacci numbers, provided no two consecutive numbers are taken. The same holds for Lucas numbers,… (More)

We consider the sequence {T n } 0 ∞ defined by
$$ {T_{n + m + 1}} = \sum\limits_{r = 0}^m {{a_r}\quad {T_{n + r}},\;n \ge 0} $$
(1)
, with initial conditions
$$ {T_r} = {c_r},\quad 0 \le… (More)

Based on Zeckendorf’s theorem concerning the unique sum-representation of any positive integer in terms of Fibonacci numbers as well as Lucas numbers /1/, the purpose of this study is the development… (More)