Pillai's problem with Padovan numbers and powers of two

Ana María García Lomeli; Santos Hernández Hernández

doi:10.15446/recolma.v53n1.81034

Publicado

2019-01-01

Pillai's problem with Padovan numbers and powers of two

El problema de Pillai con números de Padovan y potencias de dos

DOI:

https://doi.org/10.15446/recolma.v53n1.81034

Palabras clave:

Padovan sequence, Pillai's problem, linear forms in logarithms, reduction method (en)
Sucesión de Padovan, Problema de Pillai, Formas lineales en logaritmos, método de reducción (es)

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Autores/as

Ana María García Lomeli Universidad Autónoma de Zacatecas
Santos Hernández Hernández Universidad Autónoma de Zacatecas

Resumen (en)
Resumen (es)

Let (P_n)n≥0 be the Padovan sequence given by P₀ = 0, P₁ = P₂ = 1 and the recurrence formula P_n+3 = P_n+1 + P_n for all n ≥ 0. In this note we study and completely solve the Diophantine equation P_n - 2^m = P_n₁ - 2^m¹in non-negative integers (n, m, n₁, m₁).

Sea (P_n)n≥0 la sucesión de Padovan dada mediante P₀ = 0, P₁ = P₂ = 1 y la fórmula de recurrencia P_n+3 = P_n+1 + P_n para todo n ≥ 0. En esta nota estudiamos y resolvemos completamente la ecuación diofántica P_n - 2^m = P_n₁ - 2^m¹en enteros no negativos (n, m, n₁, m₁).

Referencias

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Cómo citar

APA

García Lomeli, A. M. y Hernández Hernández, S. (2019). Pillai’s problem with Padovan numbers and powers of two. Revista Colombiana de Matemáticas, 53(1), 1–14. https://doi.org/10.15446/recolma.v53n1.81034

ACM

[1]

García Lomeli, A.M. y Hernández Hernández, S. 2019. Pillai’s problem with Padovan numbers and powers of two. Revista Colombiana de Matemáticas. 53, 1 (ene. 2019), 1–14. DOI:https://doi.org/10.15446/recolma.v53n1.81034.

ACS

(1)

García Lomeli, A. M.; Hernández Hernández, S. Pillai’s problem with Padovan numbers and powers of two. rev.colomb.mat 2019, 53, 1-14.

ABNT

GARCÍA LOMELI, A. M.; HERNÁNDEZ HERNÁNDEZ, S. Pillai’s problem with Padovan numbers and powers of two. Revista Colombiana de Matemáticas, [S. l.], v. 53, n. 1, p. 1–14, 2019. DOI: 10.15446/recolma.v53n1.81034. Disponível em: https://revistas.unal.edu.co/index.php/recolma/article/view/81034. Acesso em: 1 may. 2024.

Chicago

García Lomeli, Ana María, y Santos Hernández Hernández. 2019. «Pillai’s problem with Padovan numbers and powers of two». Revista Colombiana De Matemáticas 53 (1):1-14. https://doi.org/10.15446/recolma.v53n1.81034.

Harvard

García Lomeli, A. M. y Hernández Hernández, S. (2019) «Pillai’s problem with Padovan numbers and powers of two», Revista Colombiana de Matemáticas, 53(1), pp. 1–14. doi: 10.15446/recolma.v53n1.81034.

IEEE

[1]

A. M. García Lomeli y S. Hernández Hernández, «Pillai’s problem with Padovan numbers and powers of two», rev.colomb.mat, vol. 53, n.º 1, pp. 1–14, ene. 2019.

MLA

García Lomeli, A. M., y S. Hernández Hernández. «Pillai’s problem with Padovan numbers and powers of two». Revista Colombiana de Matemáticas, vol. 53, n.º 1, enero de 2019, pp. 1-14, doi:10.15446/recolma.v53n1.81034.

Turabian

García Lomeli, Ana María, y Santos Hernández Hernández. «Pillai’s problem with Padovan numbers and powers of two». Revista Colombiana de Matemáticas 53, no. 1 (enero 1, 2019): 1–14. Accedido mayo 1, 2024. https://revistas.unal.edu.co/index.php/recolma/article/view/81034.

Vancouver

1.

García Lomeli AM, Hernández Hernández S. Pillai’s problem with Padovan numbers and powers of two. rev.colomb.mat [Internet]. 1 de enero de 2019 [citado 1 de mayo de 2024];53(1):1-14. Disponible en: https://revistas.unal.edu.co/index.php/recolma/article/view/81034

Descargar cita

CrossRef Cited-by

4

1. Mahadi Ddamulira. (2019). On the problem of Pillai with Padovan numbers and powers of 3. Studia Scientiarum Mathematicarum Hungarica, 56(3), p.364. https://doi.org/10.1556/012.2019.56.3.1435.

2. Sebastian Heintze, Robert Tichy, Ingrid Vukusic, Volker Ziegler. (2023). On the Diophantine equation 𝑈_{𝑛}-𝑏^{𝑚}=𝑐. Mathematics of Computation, 92(344), p.2825. https://doi.org/10.1090/mcom/3854.

3. Jhon J. Bravo, Maribel Díaz, Carlos A. Gómez. (2021). Pillai's problem with k-Fibonacci and Pell numbers. Journal of Difference Equations and Applications, 27(10), p.1434. https://doi.org/10.1080/10236198.2021.1990900.

4. Jonathan García, Carlos A. Gómez. (2022). On a variant of Pillai problem: integers as difference between generalized Pell numbers and perfect powers. Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas, 116(3) https://doi.org/10.1007/s13398-022-01240-6.