Solutions to a Pillai-Type Equation Involving Tribonacci Numbers and S-Units

Let \( \{T_n\}_{n\ge 0} \) ${\{T_n\}}_{n\ge 0}$ be the sequence of Tribonacci numbers. In this paper, we study the exponential Diophantine equation \(T_n-2^x3^y=c\) $T_n-2^x{3}^y=c$ , for \(n,x,y\in \mathbb {Z}_{\ge 0}\) $n,x,y\in {\mathbb{Z}}_{\ge 0}$ . In particular, we show that there is no integer c with at least six representations of the form \(T_n-2^x3^y\) $T_n-2^x{3}^y$ .