On Egyptian fractions of length 3

Autor: Enrique Treviño, Florian Luca, Francesco Pappalardi, Carlos Alexis Gómez Ruiz, Cyril Banderier

Publikováno v: Revista de la Unión Matemática Argentina
Revista de la Unión Matemática Argentina, Unión Matemática Argentina, 2021, 62 (1), pp.257-274. ⟨10.33044/revuma.1798⟩

International audience; Let a a, n, be positive integers that are relatively prime. We say that a/n can be represented as an Egyptian fraction of length k if there exist positive integers m(1), ..., m(k) such that a/n= 1/m(1) + ... + 1/m(k). Let A(k)

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::bec72e27fd1435e20419d609e2b84191
https://doi.org/10.33044/revuma.1798

Diophantine quadruples with values in k-generalized Fibonacci numbers

Autor: Florian Luca, Carlos Alexis Gómez Ruiz

Publikováno v: Mathematica Slovaca

We consider for integers k ≥ 2 the k–generalized Fibonacci sequences F (k) := ( F n ( k ) ) n ≥ 2 − k , $\begin{array}{} (F_n^{(k)})_{n\geq 2-k}, \end{array} $ whose first k terms are 0, …, 0, 1 and each term afterwards is the sum of the pr

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::7174e83315b2065f04ab543c722edd06
https://doi.org/10.1515/ms-2017-0156

Fibonacci factoriangular numbers

Autor: Florian Luca, Carlos Alexis Gómez Ruiz

Publikováno v: Indagationes Mathematicae

Let ( F m ) m ≥ 0 be the Fibonacci sequence given by F 0 = 0 , F 1 = 1 and F m + 2 = F m + 1 + F m , for all m ≥ 0 . In Castillo (2015), it is conjectured that 2 , 5 and 34 are the only Fibonacci numbers of the form n ! + n ( n + 1 ) 2 , for some

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::fc733f60bc1469f908307bc2e82e4afc
https://doi.org/10.1016/j.indag.2017.05.002

Multiplicative Diophantine equations with factors from different Lucas sequences

Autor: Carlos Alexis Gómez Ruiz, Florian Luca

Publikováno v: Journal of Number Theory. 170:282-301

Let k ≥ 2 and { u n ( 1 ) } n ≥ 0 , … , { u n ( k ) } n ≥ 0 be k different nondegenerate binary recurrent sequences of integers. In this paper, we show that under certain conditions, there are only finitely many of k-tuples of the form ( u n

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_________::db193866caea7411a962dcb00ded7a08
https://doi.org/10.1016/j.jnt.2016.06.006

On the largest prime factor of the ratio of two generalized Fibonacci numbers

Autor: Florian Luca, Carlos Alexis Gómez Ruiz

Publikováno v: Journal of Number Theory. 152:182-203

A generalization of the well-known Fibonacci sequence is the k-generalized Fibonacci sequence ( F n ( k ) ) n ≥ 2 − k for some integer k ≥ 2 , whose first k terms are 0 , … , 0 , 1 and each term afterwards is the sum of the preceding k terms.

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_________::7563dc8dbfb40192b8ce432fc47ec6bb
https://doi.org/10.1016/j.jnt.2014.11.017