33 citations · 193 across the 95 of their papers we have counts for
8 papers · 2 filters
On the separation of the roots of the generalized Fibonacci polynomial
Jonathan García, Carlos A. Gómez, Florian Luca
We prove some separation results for the roots of the generalized Fibonacci polynomials and their absolute values
Identities for the k-generalized Fibonacci sequence with negative indices and its zero-multiplicity
J. García, C. A. Gómez, F. Luca
In this paper, we prove identities for members of the k-generalized Fibonacci sequence with negative indices and we apply these identities to deduce an exact formula for its zero-m…
On the -adic zeros of the Tribonacci sequence
Yuri Bilu, Florian Luca, Joris Nieuwveld +2
In this paper, we refute some conjectures of Marques and Lengyel concerning the -adic valuations of members of the Tribonacci sequence.
On the multiplicity in Pillai's problem with Fibonacci numbers and powers of a fixed prime
Herbert Batte, Mahadi Ddamulira, Juma Kasozi +1
Let be the sequence of Fibonacci numbers and let be a prime. For an integer we write for the number of distinct representations of as…
On the transcendence of a series related to Sturmian words
Florian Luca, Joël Ouaknine, James Worrell
Let be an algebraic number with and a finite set of algebraic numbers. We study the transcendence of numbers of the form $\sum_{n=0}^\infty \frac{a_n}{b^n…
On (almost) realizable subsequences of linearly recurrent sequences
Florian Luca, Tom Ward
In this note we show that if is a simple linearly recurrent sequence of integers whose minimal recurrence of order involves only positive coefficients th…