Solvable three-dimensional product-type system of difference equations with multipliers (Q2333572)

Summary: The solvability of the following three-dimensional product-type system of difference equations \[ x_{n+1} = \alpha y_n^a z_{n-1}^b,\, y_{n+1} = \beta z_n^c x_{n-1}^d,\, z_{n+1} = \gamma x_n^f y_{n-1}^g,\, n \in \mathbb{N}_0, \] where \(a\), \(b\), \(c\), \(d\), \(f\), \(g \in \mathbb{Z}\), \(\alpha\), \(\beta\), \(\gamma \in \mathbb{C} \setminus \{0\}\) and \(x_{-i}\), \(y_{-i}\), \(z_{-i} \in \mathbb{C} \setminus \{0\}\), \(i \in \{0,1\}\), is shown. This is the first three-dimensional system of the type with multipliers for which formulas are presented for their solutions in closed form in all the cases.