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pro vyhledávání: '"LUCA, FLORIAN"'
Autor:
Alahmadi, Adel, Luca, Florian
Publikováno v:
Comptes Rendus. Mathématique, Vol 360, Iss G10, Pp 1177-1181 (2022)
In this paper, we prove the theorem announced in the title.
Externí odkaz:
https://doaj.org/article/cdabcb7411d1400b9f24c6fc31c8f748
Autor:
Filaseta, Michael, Luca, Florian
We show that if $n\ge n_0$, $b\ge 2$ are integers, $p\ge 7$ is prime and $n!-(b^p-1)/(b-1)\ge 0$, then $n!-(b^p-1)/(b-1) \ge 0.5\log\log n/\log\log\log n$. Further results are obtained, in particular for the case $n!-(b^p-1)/(b-1) < 0$.
Externí odkaz:
http://arxiv.org/abs/2411.09060
We prove that for any integers $\alpha, \beta > 1$, the existential fragment of the first-order theory of the structure $\langle \mathbb{Z}; 0,1,<, +, \alpha^{\mathbb{N}}, \beta^{\mathbb{N}}\rangle$ is decidable (where $\alpha^{\mathbb{N}}$ is the se
Externí odkaz:
http://arxiv.org/abs/2407.05191
Autor:
Bacon, Michael R., Cook, Charles K., Flórez, Rigoberto, Higuita, Robinson A., Luca, Florian, Ramírez, José L.
Inspired by the ancient spiral constructed by the greek philosopher Theodorus which is based on concatenated right triangles, we have created a spiral. In this spiral, called \emph{Fibonacci--Theodorus}, the sides of the triangles have lengths corres
Externí odkaz:
http://arxiv.org/abs/2407.07109
Autor:
Luca, Florian, Manape, Makoko Campbell
In this paper, we show that if $(U_n)_{n\ge 1}$ is any nondegenerate linearly recurrent sequence of integers whose general term is up to sign not a polynomial in $n$, then the inequality $\phi(|U_n|)\ge |U_{\phi(n)}|$ holds on a set of positive integ
Externí odkaz:
http://arxiv.org/abs/2405.11256
We consider numbers of the form $S_\beta(\boldsymbol{u}):=\sum_{n=0}^\infty \frac{u_n}{\beta^n}$, where $\boldsymbol{u}=\langle u_n \rangle_{n=0}^\infty$ is an infinite word over a finite alphabet and $\beta\in \mathbb{C}$ satisfies $|\beta|>1$. Our
Externí odkaz:
http://arxiv.org/abs/2405.05279
Autor:
Batte, Herbert, Luca, Florian
Let $ \{T_n\}_{n\geq 0} $ be the sequence of Tribonacci numbers. In this paper, we study the exponential Diophantine equation $T_n-2^x3^y=c$, for $n,x,y\in \mathbb{Z}_{\ge0}$. In particular, we show that there is no integer $c$ with at least six repr
Externí odkaz:
http://arxiv.org/abs/2403.17953
Let $ \{L_n\}_{n\geq 0} $ be the sequence of Lucas numbers. In this paper, we look at the exponential Diophantine equation $L_n-2^x3^y=c$, for $n,x,y\in \mathbb{Z}_{\ge0}$. We treat the cases $c\in -\mathbb{N}$, $c=0$ and $c\in \mathbb{N}$ independen
Externí odkaz:
http://arxiv.org/abs/2401.06555
We introduce the notion of a twisted rational zero of a non-degenerate linear recurrence sequence (LRS). We show that any non-degenerate LRS has only finitely many such twisted rational zeros. In the particular case of the Tribonacci sequence, we sho
Externí odkaz:
http://arxiv.org/abs/2401.06537
Let $(L_n^{(k)})_{n\geq 2-k}$ be the sequence of $k$-generalized Lucas numbers for some fixed integer $k\ge 2$, whose first $k$ terms are $0,\;\ldots\;,\;0,\;2,\;1$ and each term afterward is the sum of the preceding $k$ terms. In this paper, we find
Externí odkaz:
http://arxiv.org/abs/2311.14001