Seminar at SMU Delhi

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 $k\in {\mathbb Z}$. Recently, Kuhapatanakul, Anantakitpaisal, Onsri and Na nhongkai made a conjecture concerning the positive integer solutions $(m,n)$ of the Diophantine equation $$T_{m}=T_{-n}.$$ In this talk, we confirm their conjecture.

(The talk is based on joint paper with Bravo, G\'omez, Kafle, and Lucas).