• Publications
  • Influence
ON SUMS OF CERTAIN PRODUCTS OF LUCAS NUMBERS
New results about certain sums Sn(k) of products of the Lucas numbers are derived. These sums are related to the generating function of the k-th powers of the Fibonacci numbers. The sums for Sn(k)Expand
  • 7
  • 2
  • PDF
On some new identities for the Fibonomial coefficients
AbstractLet Fn be the nth Fibonacci number. The Fibonomial coefficients $$\left[ {\begin{array}{*{20}c} n \\ k \\ \end{array} } \right]_F$$ are defined for n ≥ k > 0 as follows $$\left[Expand
  • 6
  • 1
Fibonacci Numbers with a Prescribed Block of Digits
In this paper, we prove that F 22 = 17711 is the largest Fibonacci number whose decimal expansion is of the form a b … b c … c . The proof uses lower bounds for linear forms in three logarithms ofExpand
  • 7
  • 1
The p-adic order of some fibonomial coefficients whose entries are powers of p
TLDR
We show that the Fibonomial coefficient is divisible by p for all primes p such that p ≡ −2 or 2 (mod 5). Expand
  • 2
  • 1
  • PDF
On a difference equation of the second order with an exponential coefficient
Abstract This paper is devoted to a generalization of some previous results, as we completely solve a linear homogeneous difference equation of the second order with an exponential coefficient.
  • 2
  • 1
On some identities for the Fibonomial coefficients via generating function
  • P. Trojovský
  • Computer Science, Mathematics
  • Discret. Appl. Math.
  • 20 September 2007
Some new identities for the Fibonomial coefficients are derived. These identities are related to the generating function of the kth powers of the Fibonacci numbers. Proofs are based on manipulationExpand
  • 30
  • PDF
On some combinations of k-nacci numbers
Abstract For k ≥ 2, the k-generalized Fibonacci sequence ( F n ( k ) ) n is defined by the initial values 0 , 0 , … , 0 , 1 (k terms) and such that each term afterwards is the sum of the k precedingExpand
  • 2
Circulants and the factorization of the Fibonacci–like numbers
Several authors gave various factorizations of the Fibonacci and Lucas numbers. The relations are derived with the help of connections between determinants of tridiagonal matrices and the FibonacciExpand
  • 3
  • PDF
On Diophantine equations involving Lucas sequences
Abstract In this paper, we shall study the Diophantine equation un = R(m)P(m)Q(m), where un is a Lucas sequence and R, P and Q are polynomials (under weak assumptions).
  • 3
...
1
2
3
4
5
...