On a conjecture concerning the multiplicity of the Tribonacci sequence
Volume 159 / 2020
Colloquium Mathematicum 159 (2020), 61-69
MSC: Primary 11B39; Secondary 11J86.
DOI: 10.4064/cm7729-2-2019
Published online: 10 October 2019
Abstract
The Tribonacci sequence $\left \{T_{k}\right \}_{k\in {\mathbb Z}}$ is defined by $T_0=0,T_1=T_2=1$ and the recurrence $T_{k+3}=T_{k+2}+T_{k+1}+T_k$ for all $k\in {\mathbb Z}$. In 2016, Kuhapatanakul et al. made a conjecture concerning the positive integer solutions $(m,n)$ of the Diophantine equation $T_{m}=T_{-n}$. We confirm their conjecture.
