On Pillai's problem with Tribonacci numbers and powers of $2$
Bull. Korean Math. Soc. 2017 Vol. 54, No. 3, 1069-1080
https://doi.org/10.4134/BKMS.b160486
Published online May 31, 2017
Jhon J. Bravo, Florian Luca, and Karina Yaz\'an
Universidad del Cauca, Univeristy of Ostrava, Universidad del Cauca
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
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