Solutions of a Markoff type equation in the Jacobsthal- Lucas numbers
Resumen
Let $\{j_n\}_{n\geq0}$ be the sequence of Jacobsthal- Lucas number, that is given by the relation $j_0=2$, $j_1=1$, $j_n=j_{n-1}+2j_{n-2}$ for all $n\geq2$. In this paper, we study the solutions $(X,Y,Z)$ of the following equation that is so called the Jin-Schmidt equation:
\begin{equation*}
AX^2 + BY^2 +CZ^2 = DXYZ+1,
\end{equation*}
where $X=j_i$, $Y=j_j$ and $Z=j_k$ with $i,j,k\geq 1$.
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