Symmetric nonlinear solvable system of difference equations

Abstract

We show the theoretical solvability of the system of difference equations [Formula Presented], where [Formula Presented]. For several special cases of the system, we give some detailed explanations on how some formulas for their general solutions can be found in closed form, that is, we show their practical solvability. To do this, among other things, we use the theory of homogeneous linear difference equations with constant coefficients and the product-type difference equations with integer exponents, which are theoretically solvable.