Author pages are created from data sourced from our academic publisher partnerships and public sources.

Publications Influence

Share This Author

ON SUMS OF CERTAIN PRODUCTS OF LUCAS NUMBERS

- J. Seibert, P. Trojovský
- 2009

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

- D. Marques, P. Trojovský
- Mathematics
- 7 September 2014

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

- P. Trojovský
- Mathematics
- 21 April 2020

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 of… Expand

7 1

The p-adic order of some fibonomial coefficients whose entries are powers of p

- D. Marques, P. Trojovský
- Mathematics, Computer Science
- J. Integer Seq.
- 3 August 2017

TLDR

2 1- PDF

On the sum of squares of consecutive $k$-bonacci numbers which are $l$-bonacci numbers

- D. Bednarík, Gérsica Freitas, D. Marques, P. Trojovský
- Mathematics
- 2019

6 1

On a difference equation of the second order with an exponential coefficient

- P. Trojovský
- Mathematics
- 21 August 2017

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 manipulation… Expand

30- PDF

On some combinations of k-nacci numbers

- P. Trojovský
- Mathematics
- 1 April 2016

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 preceding… Expand

2

Circulants and the factorization of the Fibonacci–like numbers

- J. Seibert, P. Trojovský
- Mathematics
- 2006

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 Fibonacci… Expand

3- PDF

On Diophantine equations involving Lucas sequences

- P. Trojovský
- Mathematics
- 1 January 2019

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

...