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).

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Citas

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