We perform Lie analysis for a system of higher order difference equations with variable coefficients and derive non-trivial symmetries. We use these symmetries to find exact formulas for the solutions in terms of k. Furthermore, a detailed study for a specific value of k is presented. Our findings generalize some results in the literature.

In this work, group theory is applied to obtain generators of the Lie algebra for a class of rational difference equations of order k + l where k and l are positive integers. This is followed by deriving invariants and solutions via some linear recurrences and with the introduction of some number-theoretic arithmetical functions. Furthermore, sufficient conditions for the existence of solutions for periods two and four are provided in special cases. The results in this paper generalize certain known results.