On Pillai's problem with Tribonacci numbers and powers of $2$

Jhon J. Bravo; Florian Luca; Karina Yaz\'an

doi:10.4134/BKMS.b160486

Bulletin of the
Korean Mathematical Society BKMS

ISSN(Print) 1015-8634 ISSN(Online) 2234-3016

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Bull. Korean Math. Soc. 2017; 54(3): 1069-1080

Online first article January 25, 2017 Printed May 31, 2017

https://doi.org/10.4134/BKMS.b160486

On Pillai's problem with Tribonacci numbers and powers of $2$

Jhon J. Bravo, Florian Luca, and Karina Yaz\'an

Universidad del Cauca, Univeristy of Ostrava, Universidad del Cauca

Abstract

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Abstract

The Tribonacci sequence $\{T_n\}_{n\ge 0}$ resembles the Fibonacci sequence in that it starts with the values $0,1,1,$ and each term afterwards is the sum of the preceding three terms. In this paper, we find all integers $c$ having at least two representations as a difference between a Tribonacci number and a power of $2$. This paper continues the previous work \cite{DLR16}.

Keywords: Tribonacci numbers, linear forms in logarithms, reduction method

MSC numbers: 11B39, 11J86