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pro vyhledávání: '"Tron, Emanuele"'
Sequences of the form $(\gcd(u_n,v_n))_{n \in \mathbb N}$, with $(u_n)_n$, $(v_n)_n$ sums of $S$-units, have been considered by several authors. The study of $\gcd(n,u_n)$ corresponds, following Silverman, to divisibility sequences arising from the s
Externí odkaz:
http://arxiv.org/abs/2408.05820
Pila and Tsimerman proved in 2017 that for every $k$ there exists at most finitely many $k$-tuples $(x_1,\ldots, x_k)$ of distinct non-zero singular moduli with the property "$x_1, \ldots,x_k$ are multiplicatively dependent, but any proper subset of
Externí odkaz:
http://arxiv.org/abs/2207.05183
Autor:
Sanna, Carlo, Tron, Emanuele
Publikováno v:
Indagationes Mathematicae 29 (2018), 972-980
For each positive integer $k$, let $\mathscr{A}_k$ be the set of all positive integers $n$ such that $\gcd(n, F_n) = k$, where $F_n$ denotes the $n$th Fibonacci number. We prove that the asymptotic density of $\mathscr{A}_k$ exists and is equal to $$
Externí odkaz:
http://arxiv.org/abs/1705.01805
Autor:
Luca, Florian, Tron, Emanuele
Consider the positive integers $n$ such that $n$ divides the $n$-th Fibonacci number, and their counting function $A$. We prove that \[A(x) \leq x^{1-(1/2+o(1))\log\log\log x/\log\log x}.\]
Comment: 8 pages. 1/4 improved to 1/2. To appear in the
Comment: 8 pages. 1/4 improved to 1/2. To appear in the
Externí odkaz:
http://arxiv.org/abs/1410.2489
Autor:
Tron, Emanuele
In this note we prove that, if $S_n$ is the greatest area of a rectangle which can be covered with $n$ unit disks, then $2\leq S_n/n<3 \sqrt{3}/2$, and these are the best constants; moreover, for $\Delta(n):=(3\sqrt{3}/2)n-S_n$, we have $0.727384<\li
Externí odkaz:
http://arxiv.org/abs/1409.4545
Autor:
Sanna, Carlo, Tron, Emanuele
Publikováno v:
In Indagationes Mathematicae June 2018 29(3):972-980
Autor:
Tron, Emanuele
Publikováno v:
Rendiconti del Seminario Matematico
Rendiconti del Seminario Matematico, Università degli studi di Torino / Politecnico di Torino, 2020
Rendiconti del Seminario Matematico, Università degli studi di Torino / Politecnico di Torino, 2020
International audience; We survey the existing theory on the greatest common divisor gcd(u_n,v_n) of two linear recurrence sequences (u_n)_n and (v_n)_n , with focus on recent development in the case where one of the two sequences is polynomial.
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=dedup_wf_001::10b620d8422b6bed5566bc2409eb0d5d
http://hdl.handle.net/20.500.12278/113100
http://hdl.handle.net/20.500.12278/113100
Autor:
Sanna, Carlo, Tron, Emanuele
Publikováno v:
Indagationes Mathematicae
Indagationes Mathematicae, Elsevier, 2018, 29 (3), pp.972-980. ⟨10.1016/j.indag.2018.03.002⟩
Indagationes Mathematicae, Elsevier, 2018, 29 (3), pp.972-980. ⟨10.1016/j.indag.2018.03.002⟩
For each positive integer $k$, let $\mathscr{A}_k$ be the set of all positive integers $n$ such that $\gcd(n, F_n) = k$, where $F_n$ denotes the $n$th Fibonacci number. We prove that the asymptotic density of $\mathscr{A}_k$ exists and is equal to $$
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::411389173bf9e978580ccc63ae355105
https://hal.archives-ouvertes.fr/hal-02491415
https://hal.archives-ouvertes.fr/hal-02491415
Autor:
Luca, Florian, Tron, Emanuele
Publikováno v:
Advances in the Theory of Numbers; 2015, p149-158, 10p