Solvable Three-Dimensional Product-Type System of Difference Equations with Multipliers

The solvability of the following three-dimensional product-type system of difference equations x n + 1 = α y n a z n − 1 b , y n + 1 = β z n c x n − 1 d , z n + 1 = γ x n f y n − 1 g , n ∈ N 0 , where a , b , c , d , f , g ∈ Z , α , β , γ ∈ C { 0 } and x − i , y − i , z − i ∈ C { 0 } , i ∈ { 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